Obtaining flux estimates nevertheless still required frequent manual reinitalization to obtain a good reproduction of the experimental data and, moreover, did not optimize on all observables simultaneously (metabolites and isotopomer concentrations). In our contribution we focus on measures to achieve faster and robust dynamic flux estimation which leads to a high dimensional parameter estimation problem. Specifically, we address the following challenges within the PWA problem formulation: (1) Fast selection of sufficient domains for the PWA flux functions, (2) Control of over-fitting in the concentration space using shape-prescriptive modeling and (3) robust and efficient implementation of the parameter estimation using the hybrid implicit filtering algorithm. With the improvements we significantly speed up the convergence by efficiently exploiting that the optimization problem is partly linear. This allows application to larger-scale metabolic networks and demonstrates that the proposed approach is not purely theoretical, but also applicable in practice.The design of microbial production processes relies on rational choices for metabolic engineering of the production host and the process conditions. These require a systematic and quantitative understanding of cellular regulation. Therefore, a novel method for dynamic flux identification using quantitative metabolomics and  Thesein vitro, but the validity of estimated kinetic parameters has been shown to be limited for reconstruction of the observed in vivo metabolic network properties [In vivo, only the whole network response can be analyzed, making the identification of kinetics highly challenging. Pioneering in vivo research [Kinetic metabolic regulation is a result of complex interactions between enzymes, substrates and allosteric effectors. Enzyme kinetics can be investigated operties . In vivoresearch  used stie), substrate and effector concentrations (ci) and kinetic parameters (θ) and are typically non-linear. The latter can be either derived from mechanistic assumptions e.g., Michaelis-Menten kinetics, or be non-mechanistic e.g., power law leading to parameters with no physical meaning [These models use kinetic formalisms to describe the flux as a function of enzyme activity ( meaning .(1)v=e⋅(1)The model equations  are strongly dependent on each other, which means the system can hardly be solved from a decomposition and commonly also leads to highly correlated parameters ,9.(2)a priori, which means that the mechanism of every enzyme and all interactions between metabolites and enzymes involved in the regarded metabolic network have to be selected before parameter optimization. Especially, the kinetic formats of each reaction in larger metabolic networks are yet unknown, unclear, or shall be deduced from the captured observables.The kinetic functions have to be chosen There are mainly two inherent conceptual drawbacks of kinetic modeling:i.e., the nullspace, however, the methodology requires selecting a kinetic model a priori and cannot directly identify dynamic metabolic fluxes. Regardless of those challenges, the number of uncertain reaction mechanisms in a kinetic model leads to a rapidly increasing number of models to be compared, together with the challenges of parameter estimation in non-linear systems, which result in putative non-convex optimization landscapes that quickly reach computationally infeasible scales.One solution that has been used to address this issue was to define a family of different models, also referred to as ensemble modeling ,11,12,13a priori assumptions of kinetics  strong enough to cover a significant (metabolite) concentration space for good identification of the kinetic parameters .•The metabolomics should preferably have a complete coverage of the regarded intracellular metabolic response, e.g., intracellular concentrations, which moreover have to be quantitative.•13C labeled substrate for improved flux tracing, as the concentration information alone is mostly not sufficient to identify all intracellular fluxes [Use of a r fluxes ,23.Crucial for every modeling approach is sufficient information for the identification of the model parameters from the observables . The idedy-state  and the 13C labeled internal standards [13C enrichment information.These experimental requirements are partly conflicting, especially when concentration measurements are performed using tandards , as they(1)13C labeling from a single experiment.They generate repetitive concentration patterns in time, allowing for dense sampling from multiple cycles as well as application of (2)The feast/famine perturbation includes both: the transient from limitation to excess as well as a return to limitation in a short timeframe of minutes.(3)In this setup, the starting metabolite concentrations of each cycle are the same as the endpoint, which means there is no net metabolite accumulation during one cycle .In this work, we build on one dynamic setup that has been demonstrated to be advantageous in facilitating concentration and labeling measurements—there cyclic and block-wise feeding are used leading to so-called feast-famine conditions ,26. Compi.e., improving data density and accuracy.These properties are beneficial for flux identification, as the concentration and enrichment information can be captured over several cycles, In the piecewise affine flux estimation approach, the choice of the number and positions of the breakpoints is crucial for a successful approximation of the flux profile in time and they directly determine the achievable convergence of the flux approximation towards the real fluxes as well as the number of parameters to be identified from the observables.The method requires that the breakpoints for all flux functions in the metabolic network have the same set of breakpoints. To best capture the different response of all the metabolites and fluxes a satisfying compromise of breakpoints has to be found. Changes in the (net) in- and out-fluxes of a metabolite pool influence the metabolite concentration and it is assumed that the major changes in metabolic (net) fluxes are reflected if the flux approximation can reproduce the concentration profile well.13C labeling aside. If the reproduction of enrichment measurement is not satisfactory, additional domains can be introduced at any time in the optimization workflow. Moreover, a trade-off between the number of parameters to be estimated and the convergence that can be achieved with the PWA flux functions has to be found. Especially, a too high number of breakpoints can significantly increase the tendency of the system towards overfitting.With this assumption, an optimization for the placement of breakpoints (number and times) can be performed using the less complex linear metabolite balances and the concentration observables leaving the in silico data, the properties of the domain selection are studied. A small reaction network, further referred to as the spiral model, is simulated under feast-famine conditions and the approximation is compared to the noise-free measurements of the model with respect to:(1)The number of breakpoints and(2)The placement of breakpoints.Using t = 126 s) reduces the sum of squares about fourfold (134.1). Nevertheless, the approximation of the concentration profiles is visually not yet sufficient. To compare the goodness of fit we use the R2 and adjusted t0 = 0 s and endt = 140 s). Further, the Akaike information criterion (AIC) is calculated and summarized in R2 = 0.77).In the spiral network, six metabolite pools are observed  at 13 different time points during a feast/famine cycle of 140 s. The first and last breakpoints are fixed . With only these breakpoints, no reasonable approximation can be obtained see  and the t2 = 25 s, t3 = 131 s), a sum of squares of 15.1 (R2 = 0.97) is reached and the concentration measurements can be reproduced within the expected error range of 10%. Addition of another, third free breakpoint further reduces the RSS to 2.3 (R2 = 0.99). Next to these global optima, local minima are observed.With a second free breakpoint (best choice t2 = 23 s and t3 = 132 s (RSS = 16.9). The territory of approximation error (RSS) has several local minima (data not shown). The second best combination of breakpoints was obtained with t2 = 2 s and t3 = 30 s (RSS 25.3).When two free breakpoints are placed, the best combination was obtained with R2 = 0.996) is found for a combination with t = , the second cluster has a minimum of 4.6 at t2 = 2 s, t3 = 14 s, t4 = 83 s  laborious and computationally hardly feasible on standard computer hardware. From a practical standpoint, it is desirable to start with a simple model, as extension of a model is usually more straightforward than a model reduction, moreover, a smaller number of parameters can often be better identified from the observables [Clearly, the breakpoint optimization will lead to an optimal sequence of breakpoints for the flux functions in terms of the chosen objective function Rervables .2 or AIC, can help in finding a minimal set of breakpoints. However, also using those criteria does not necessarily guarantee a sufficient representation of the concentrations, i.e., occurrence of overfitting and no negative concentrations. Having in mind those practical limitations of the domain selection, we implemented constraints in the approach that allow computing flux functions, even with a suboptimal choice of breakpoints and shape-prescriptive constraints.Here the use of objective functions penalizing the number of parameters, like adjusted Rt =  is discussed. Two major flaws can be observed  Metabolite A shows overfitting in the last domain. Negative concentrations are undoubtedly not feasible and cannot be accepted; moreover they compromise the numerical integration of the isotopomer balances being detrimental to the numerical robustness of the forward simulation. To enforce non-negativity quadratic inequality, constraints are introduced. This measure prevented all metabolites to reach negative concentrations  Neguxes see . MoreoveP. chrysogenum was re-evaluated. The metabolic network for flux identification, further referred to as PenG model, comprises 17 balanced metabolites and 28 fluxes. Five free breakpoints were determined, leading to a total of seven breakpoints, i.e., t = (0 s 18 s 36 s 90 s 185 s 230.5 s 360 s). Because of the dependency of the last and first domain (feast/famine setup), 28 × 6 = 168 flux values need to be estimated.To demonstrate the practical performance of the optimization approach, a previously described dynamic labeling experiment with The simulations have been performed over three consecutive feast/famine cycles. As a starting point for the parameter optimization, a feasible parameter set derived from the best fit for the metabolite concentration measurements (including the respective constraints) was used.We first applied a damped Quasi Newton optimization algorithm as reference convergence performance . We founNull-space-based sampling indeed significantly increases the convergence  and shapi.e., the gradients become very small. This inefficiency could be reduced by the implementation of a threshold for the improvement between subsequent iterations Indeed, this measure  improves the convergence significantly, especially for the first couple of iterations. However, it has to be noted that the thresholds can increase the risk of obtaining a local optimum. The strategy that has been implemented to prevent such behavior is to restart the complete sequence of stencil scales after failure of a stencil.It can be observed that the implicit filtering algorithm leads to a step-wise convergence . This beThe flux estimation follows a workflow, which will be described in detail in the following subchapters. First step is the domain selection procedure selecting the breakpoints for the flux functions. This is followed by definition and introduction of the non-negativity (prevents negative concentrations) and shape-prescriptive constraints. For use of the final step, first a feasible initial iterate has to be computed as implicit filtering requires this as an input. The final step performs the actual flux identification with incorporation of the enrichment data.in silico Spiral model was used as described previously [The eviously .−1. The feed contained minimal medium with a glucose concentration of 15 g/L. After several cycles, repetitive offgas and DO measurements were obtained, a biomass concentration of 5.7 g/L was obtained (average over the cycle). Samples for intracellular metabolites were withdrawn using a rapid-sampling device [13C-labeled glucose. The enrichment was monitored during three consecutive cycles using rapid sampling and MS analysis.For the practical PenG example, concentration and labeling measurements as well as the metabolic network stoichiometry were obtained from a feast/famine cultivation of P. chrysogenum as previously reported . In brieg device , quencheg device ,28. AfteN.The modeling approach is based on balances for metabolite concentrations and enrichments quantified by isotopomers  ,29. For g can be derived describing the balance of each single isotopomer concentration  x of the network:Based on the atom transitions and the stoichiometry, a non-linear function i.e., mass-isotopomer fractions.Integration of the isotopomer balances will yield the time-course of the isotopomer concentrations, which can be used to calculate the observables, j valid for all fluxes in the considered metabolic network, partitioning the flux function vi into number of breakpoints minus one domains in time:Using piece-wise affine functions for the flux description changes some properties of the equation system. The piece-wise affine flux functions are defined in time by a set of breakpoints ti at the breakpoint tj and defined strictly positive (so a reversible reaction will have two fluxes). Flux values between breakpoints are calculated by linear interpolation on its two adjacent breakpoints. Therefore a metabolic network with i fluxes and j breakpoints has i × j parameters to be estimated. As will be discussed later, this number can decrease for specific experimental setups that introduce additional constraints on the concentrations or flux functions. This definition is also valid for higher order piecewise-defined flux functions as long as they are to be defined unique on the breakpoints, e.g., smooth quadratic splines, but will not be discussed in the scope of this paper.The parameters of this function are the value of respective fluxes vj by linear combinations according to the stoichiometry matrix which can be further divided into known bv and unknown nv fluxes [With the previous definition of the flux functions in time, the metabolite mass balances can be formulated locally at every breakpoint n fluxes .(5)N=[Nn is square and nondegenerate, the matrix can be inverted and a unique solution of unknown fluxes can be identified from the concentration transients and the known fluxes.If Ni.e., they contain parallel pathways, cycles or reversible reactions.In practice most metabolic networks are underdetermined with respect to the number of unknown fluxes f, This means the metabolic network does not contain enough measurable (known) fluxes in order to identify all fluxes. In this case Nn spans a null space (kernel), which contains all linear combinations of its basis vector(s) describing the infinite combinations of fluxes that lead to the same solution of This is called practical non-identifiability and also directly explains why isotopic tracers are needed in order to identify all flux functions of such metabolic networks.v, thus u on the same breakpoints as v:The right hand side (rhs) c0:This function can easily be integrated , leading to a continuous, quadratic solution for the concentration in time with the initial concentrations i,ju; with available concentration measurements, a linear regression can be performed to obtain the best estimate of u. The measurements cM at timepoints tM can be obtained by generation of a matrix Y:As can be seen, this solution is moreover linear with respect to WM) then reads:The weighted linear regression problem (with weight matrix Solving the optimization problem13C tracer.) with the inner loop solving Equation (12). and the outer loop iterating on the breakpoints minimizing the weighted residual sum of squares on the concentration observables Rc using the PSwarm optimization algorithm [For the flux functions the location of the breakpoints in time has to be selected as also derived in . Best prlgorithm   can lead to issues during the optimization. Especially, cases that impair the stability of the numerical integration have to be prevented to ensure maximal robustness of the high-dimensional parameter estimation: (1) Negative values in the approximation of the concentration profile; (2) Overfitting. Additionally, the experimental setup could enforce certain conditions that should be reflected in the parameter estimation, like in the case of the feast/famine setup, the first and last domain (beginning and end of the cycle) have to be equal.(1)In a stable feast-famine regime the metabolite concentration at the end of one cycle has the same concentration as in the beginning (of the next cycle).(2)Similarly, the flux at the end of the feast famine cycle has to be the same as in the beginning. Otherwise no stable, repetitive cycles were obtained.In the previous paragraph, the solution for the best estimate of the concentration profile with the given breakpoints has been demonstrated. In the special case of a feast/famine experiment the solution should additionally fulfill two (linear) constraints:u (and c0). A column vector C is generated, representing a column of matrix Y for the timepoint endt:The concentration at the end of the cycle is the result of the integration using the parameters Integration of the constraint is obtained using Lagrange multipliers λ:v1 = vj. The vector C (and b) are extended by an additional row:A comparable approach is taken to introduce the flux constraint As can be seen this equality constraint reduces the number of parameters by one per balanced metabolite.In order to ensure numerical stability of the integration for the isotopomer equations, it is crucial that computed negative approximated concentrations are detected and eliminated. In order to find a sufficient constraint the piecewise quadratic concentration pattern has to be evaluated in every domain. In the convex case, the minimum of the vertex value has been computed, whereas in the concave case it has to be checked for roots in its interval. These computations are trivial but correspond to a nonlinear (quadratic) inequality constraint.In practical applications overfitting has to be prevented. Reasons for overfitting can be (1) noisy data, (2) outlier or leverage points, (3) suboptimal choice of domains for flux functions, (4) suboptimal sample time points, (5) systematic error in observables or (6) missing data. Overfitting will lead to flux functions with potentially too high gradients. Additionally, because metabolite pools are often closely linked, the overfitting will propagate through the metabolic network, leading to an ill-posed optimization landscape hindering the parameter estimation progression and biased flux functions.One obvious approach is to optimize the domain selection as discussed. Nevertheless, there are limits to the reduction of domains as all flux functions are defined on the same domains, and a trade-off between overfitting prevention and achievable convergence of the flux functions has to be found. It has to be noted that the proposed linear solution of the domain selection can only be applied to a subset of the observables (the concentration measurements), while non-linear differential equation systems are required to obtain the labeling profile. Consequently, the domains are chosen on a subset of the available data leading to a risk that the domain selection yields a good approximation but potentially not the global optimum for all data.Shape constraints can be applied to “guide” the optimization procedure using shape primitives; together with the least squares objective function. This additional information on the shape of the (quadratic) concentration patterns has several benefits:(1) It can facilitate higher convergence orders of the flux functions; (2) The constraints restrict the search space and prevent that the optimization algorithm to converge in local optima in a noisy optimization landscape; (3) The chosen constraints do not introduce additional (unobserved) parameters; (4) The evaluation of the constraints is computationally very cheap even at large scale.Shape constraints are (with exception of the non-negativity constraint) linear inequality equations, which can be implemented rapidly and intuitive in the PWA framework as linear inequality constraints on the parameter vector. This also means that feasible parameter sets can be computed almost instantly using linear programming. It has to be noted that shape constraints can also be introduced for metabolites where no observables are on hand  which are exceptionally prone to overfitting as they do not contribute to the objective function. A strategy that has been used in the Penicillium model was to assume non-observed pools to follow the same dynamics as their surrounding metabolites.u at the breakpoints adjacent to the respective domain.When constraining the monotonicity in a domain four cases have to be considered for PWA flux functions: (1) Monotonous decreasing, (2) Monotonous increasing, (3) Switch from monotonous increasing to monotonous decreasing and (4) Switch from monotonous decreasing to monotonous increasing See . In the i.e., forcing the inflection point to the respective middle knot. Generally, convexity and curvature can be constrained independently. Nevertheless, in the case that a change of monotonicity is enforced, also the curvature is constrained. It is good practice to check the constraints for feasibility, e.g., by using a linear programming solver, e.g., linprog in MATLAB.A direct switch from monotonous increasing to decreasing and the other way round is only possible if the rhs between those neighboring domains was zero, leading to a double-inequality constraint which is equivalent to an equality constraint, In special cases a more stringent constraint than the inequality constraints could be needed. Here, the slope of the concentrations at the breakpoints can also directly be constrained using an equality constraint:i.e., the (net) influx equals the outflux at all times  was chosen, whereas a constant a was introduced as scaling factor to weight the two iR, which will lead to different points on the respective pareto frontier; it has been set to 1.317 to normalize for the different number of observations in either dataset. This leads to a multi-objective optimization problem and the L2 global criterion was used to define the overall objective function on previously computed aspiration values (best fit on either dataset) for the two residual sum of squares (cR and xR).The final flux (parameter) estimation problem has to minimize the error subject to two sets of objectives: (1) The concentration measurements and (2) The Computing the aspiration values on first sight seems an unnecessary additional effort, but it has to be noted that the best fit of the concentration data is already available from the domain selection procedure and a good approximation of the enrichments can usually be computed fast, neglecting the concentration observables.In practice this has the advantage that the whole dataset can be inspected for outliers and leverage values and those observations can be removed or downweighted. This procedure will lead to a better posed optimization landscape and can speed up the overall parameter estimation process considerably. If no good estimate for the errors is available, those could also be estimated using, e.g., an iteratively reweighted least squares approach like robust regression. With the current scope to analyze the practical optimization convergence, a simplifying assumption of an error of 5% of the average value within each dataset was used.stencil  in the parameter space comparable to a pattern search or direct search algorithm. From the collected points in the iteration, projected gradients are computed, which are then used to perform a quasi-Newton iteration. In case no improvement was found using the quasi-Newton iteration, the solver will move the center of the stencil to the best sampled point. If no better point was sampled, the actual stencil scale is adjusted (decreased) or the optimization is terminated. In this work, the quasi-Newton iteration with the SR1 Hessian update was used.The implicit filtering algorithm has been applied as provided (version for MATLAB)  with minImfil has to be initialized with a strictly feasible initial parameter set, which was computed using the MATLAB fmincon solver. In contrast to fmincon, using imfil, constraints have to be implemented as so-called hidden constraints, i.e., a parameter set outside the feasible territory is rejected and a failure is returned to the algorithm  are likely to lead to a better value in objective function and (2) are known to fulfill the given constraints together with the central finite differences. Feasible directions have been implemented in the algorithm using the A powerful set of such directions can be directly derived from Equation (7). Samples within this null space will have the same rhs u, and therewith the concentration profile as the current best iterate, but still a different solution of the isotopomer balances. Using this stoichiometry-based null space is further referred to as null-space-based sampling.13C labeling measurements to be identified. This parameter space reduction also eliminates the putative trade-off between concentration and enrichment observable residuals in the multi-objective function . In order to find the best overall optimum on all observables the central finite differences for all parameters are sampled together with the null space basis vectors.This approach allows iterating in the lower dimensional space of fluxes (parameters) see , which cDynamic flux identification requires advanced experimental and computational approaches, especially experimental setups that allow for the simultaneous, respective serial measurement of intracellular concentrations and labeling enrichments. For the evaluation and interpretation of this experimental data, modeling and parameter estimation are crucial and require attention to obtain a good approximation of metabolic network fluxes.Metabolic networks show an inherent correlation of (flux) parameters and common optimization approaches fail to identify the proper search direction. To solve this issue, we applied PWA flux functions and a two-staged optimization that resulted to be feasible also for larger networks. Especially, the implementation of implicit filtering-based optimization algorithms increased the convergence speed and basically eliminates manual intervention by frequent re-initialization of the optimization. The proposed implementation allowed for the obtaining of a reasonable estimate for 168 parameters within 20,000 function evaluations. Key for fast convergence were (1) implementation of null space sampling and (2) shape constraints that prevent overfitting and reduce the search space.i.e., each approximated flux profile can be reproduced and tested using different kinetics formats for a small network as discussed in [Once the flux functions in time have been identified, these together with the respective effector concentration measurements allow for testing of different biological hypothesis on the regulatory mechanism. In contrast to the classical reaction kinetic approach, the identification of kinetic parameters can now be decoupled from the overall metabolic network, ussed in .


Over the last years, several methods for the phenotype simulation of microorganisms, under specified genetic and environmental conditions have been proposed, in the context of Metabolic Engineering (ME). These methods provided insight on the functioning of microbial metabolism and played a key role in the design of genetic modifications that can lead to strains of industrial interest. On the other hand, in the context of Systems Biology research, biological network visualization has reinforced its role as a core tool in understanding biological processes. However, it has been scarcely used to foster ME related methods, in spite of the acknowledged potential.In this work, an open-source software that aims to fill the gap between ME and metabolic network visualization is proposed, in the form of a plugin to the OptFlux ME platform. The framework is based on an abstract layer, where the network is represented as a bipartite graph containing minimal information about the underlying entities and their desired relative placement. The framework provides input/output support for networks specified in standard formats, such as XGMML, SBGN or SBML, providing a connection to genome-scale metabolic models. An user-interface makes it possible to edit, manipulate and query nodes in the network, providing tools to visualize diverse effects, including visual filters and aspect changing . These tools are particularly interesting for ME, since they allow overlaying phenotype simulation results or elementary flux modes over the networks.The framework and its source code are freely available, together with documentation and other resources, being illustrated with well documented case studies.The online version of this article (doi:10.1186/s12859-014-0420-0) contains supplementary material, which is available to authorized users. Within the field of Systems Biology, the analysis of different types of biological networks is an important task in understanding the underlying biological processes. For this endeavour, a mathematical framework is provided by graph theory, which has allowed to verify that a multitude of organisms share relevant properties when analysing the topology of their networks . AdditioTogether with their regulatory  and signMetabolic Engineering (ME) aims to rationally pinpoint genetic changes in selected host microbes that can optimize the production of compounds of industrial interest and, thus, it heavily makes use of computational analyses of metabolic networks. However, in many cases, the static view of metabolic systems provided by these networks is insufficient, and there is the need to reconstruct genome scale metabolic models (GSMMs)  with simGiven the lack of kinetic information to provide for large-scale dynamical models, stoichiometric models are the most common. The information about the metabolites and reactions from the metabolic network, together with stoichiometry, are the starting points for their reconstruction , being mGSMMs are often used to simulate the metabolism of the cell using constraint-based approaches, where typically a pseudo steady state is assumed . Using tIn this work, an integration of network visualization with ME methods is proposed, which demands that many issues related with the visualization of metabolic networks must be addressed. While the scalability of the networks is successfully addressed by generic visualization packages, usually the generic layouts available produce unsatisfactory results for metabolic networks. This is mostly due to the fact that the majority of layout algorithms do not take into consideration any biological knowledge, such as cell localization or molecular functions. Another problem comes with the filtering of the networks. It is necessary to have an easy way to query the network and visually filtering it to specific sets of nodes of interest in a given context. To address these problems, a visualization tool should offer some basic features: layout algorithms, a graphical notation, integration with analysis tools by providing information about the network and an user interface to allow interaction .OptFlux [COBRA Toolbox [CellNetAnalyzer [FASIMU [CellDesigner [There are a myriad of software tools for ME, able to use metabolic models to perform phenotype simulations and implement strain optimization methods, being some of the best known examples: OptFlux , the COB Toolbox ,13, CellAnalyzer  and FASI [FASIMU . There aDesigner ,17, for Cytoscape [FluxViz [FluxViz was primarily developed for FASIMU, a software for flux-balance computation, and it uses the generated result files as input for visualization.ytoscape  became a[FluxViz , provideVANTED [FluxMap, that allows the visualization of measured or simulated fluxes in the network, and FBASimVis for constraint-based analysis of metabolic models, with a special focus on the dynamics and visual exploration of metabolic flux data resulting from model analysis. It supports wild type and knock-out FBA simulations.Another tool worth mentioning is VANTED , an applCOBRA toolbox and CellNetAnalyzer are based on the commercial software Matlab, and therefore are not freely available for the community. COBRA already includes some network visualization tools in the original release, but the generated maps are static built-in maps, that can be exported in a single format (SVG), optionally including overlaps with simulation results. An extension, Paint4Net [BiGG database, editing options are quite limited and layouts can only be exported as images and not reused. On the other hand, CellNetAnalyzer only enables the visualization of small or medium scale biological networks. More recently, MetDraw [Both the aint4Net , that al MetDraw , that isIn the majority of these tools, biological entities/ interactions are represented as shapes/ lines, with different colours/formats standing for their classes. Although this seems a reasonable solution, the complexity of the integrated information and the range of possible interactions motivated the development of standard notations. The most successful was the Systems Biology Graphical Notation (SBGN) , where nOptFlux platform, allowing its integration with other tools, building a useful tool to assist ME researchers. To highlight the main features of the tool, described in detail next, as compared to the other tools, Table Overall, and in spite of the aforementioned tools, network visualization has been traditionally apart from ME-related methods. Some notable exceptions were already mentioned, but an effective framework, which would facilitate the agile integration of simulation results with dynamic layouts of metabolic networks, is, in the authors’ point of view, still lacking. Indeed, this work focuses on the development of a visualization framework based on a well-defined abstract representation of metabolic networks, which will provide researchers with visualization tools, to be used in the context of ME projects. This has been developed as a plugin for the Metabolism can be represented as a series of transformations of metabolites, being easy to represent as a graph. There are two main entities that will be addressed by the visualization platform: reactions and metabolites. A reaction is a chemical transformation that uses a set of metabolites as reactants and produces another set of metabolites to be used by other reactions.For the representation, a reaction-compound network Figure A was choA metabolic layout can then be defined by a core list of reactions, each represented by a reaction node, a set of reactants, a set of products and a set of information nodes. The reactants and products are represented as sets of metabolite nodes, representing the compounds that are part of that specific chemical reaction. The reaction node, and the respective metabolite nodes, will be connected by edges, represented as lines with a shape defined according to the reversibility of the reaction. If the reaction is irreversible, the edges that connect reactions to the metabolites will have arrows only pointing to the products Figure B, while A metabolic layout is based on the reactions contained in the metabolic model. Since one of the goals of this work is to provide a link between the visualization and the metabolic model, a strategy must be defined to map the entities of the visualization framework with the entities of the model. It is also desirable that a layout can represent just a part of the metabolism of an organism , as well as the possibility to use the same layout on different models (e.g. different strains or model versions). Another important aspect is to make networks visually more understandable, replicating some of the nodes, a feature typically applied to currency metabolites. To comply with these features, each reaction and metabolite node will have a list of model identifiers that will provide the link between the model and the layout.Visualization layer: provides all the functionalities related with the visualization and edition of a layout, including automatic layouts, creation and edition of layouts, visual filters and operations to change the aspect of the network .Input and output layer: implements several tools that provide network creation and exportation capabilities for a multitude of file formats. It has the objective of reading networks in specific file formats and building the metabolic layout, used by the visualization layer. At the same time, it also provides the possibility to export those layouts into some of those formats.The two main tasks of the software are to build these layouts from external sources (being able to export them as well), and to visually represent them. This leads to a two-layer architecture Figure , where tOptFlux in this case) was facilitated. This brings to light the importance of the MVC (model-view-controller) design pattern, not only in the development of the framework, but also in the integration with OptFlux, that also follows this principle. Indeed, OptFlux is built on top of AIBench (http://www.aibench.org/), a software development framework developed by researchers from the University of Vigo in Spain. Building applications over AIBench facilitates the creation of applications composed of units of work with high coherence that can easily be combined and reused, by incorporating three main object types: operations, datatypes and datatype views.The strategy adopted in the development of the framework had the goal of creating a tool that can be used independently, but at the same time build it in a way such that the integration with an ME tool , strain optimization algorithms and with many other features. It also contains all data structures and methods used to represent metabolic models, and reading/writing files in different formats. OptFlux’s plugin-based architecture facilitates the development of additional features. The visualization plugin is such an example, which provides a direct connection between the metabolic model, simulation and optimization methods used in OptFlux, and the metabolic layout defined in the visualization core framework.The basis of the implementation of the operations in prefuse package (http://prefuse.org/), the CD-SBML is read using JSBML [libSBGN [Batik Java SVG Toolkit (http://xmlgraphics.apache.org/batik/) and VectorGraphics2D (http://trac.erichseifert.de/vectorgraphics2d/).The entire visualization framework was developed in Java. The visualization of the graph is done using the ng JSBML , SBGN-ML[libSBGN  and the As stated previously, the visualization layer provides all the functionalities related with the visualization and editing of the metabolic layout. One of these features allows to change the default colours and shapes of the nodes. The graphical user interface (GUI) is composed of two major elements Figure : the netThis layer provides all the features that allow navigating and obtaining additional information about the network by clicking the nodes. Some of them are the basic features that are typical in any visualization framework, such as highlighting, zooming and dragging, which allow navigating through the network. By clicking a node, the node information panel will display information on that node. It is possible for advanced users to implement an information panel and add it to the interface, to visualize information of specific interest.Force Directed Layout (FDL) [One of the main features allows loading layouts from different sources. Some layouts may not specify the coordinates of (some of) the nodes. The layout used by the visualizer, by default, is the ut (FDL)  with somAnother crucial aspect is the ability to edit the metabolic layout. This feature, when combined with the import and export capabilities, provides users with the means to create and edit their layouts, being able to export them for later use.As stated above, the same metabolite can be represented several times in a layout by different nodes. If a metabolite node is connected by several reactions the user can replicate it, resulting in a metabolite node for each reaction. Also, metabolite nodes representing the same compound can be merged. It is also possible to replicate a reaction node, resulting in two, or more, reactions connected to the same set of metabolite nodes. Merging two reactions is only possible if they are exactly the same, i.e. are connected to the same nodes and have the same reversibility. The type of a metabolite can be changed, e.g. to a currency metabolite.Filtering and overlaying capabilities are also provided. It is possible to filter the network, by hiding parts of it, based in the node type  or by reaction identifier. To overlay information over the network, the visualizer allows altering its visual aspect, supporting the change of the direction, thickness and colours of the edges, while for nodes it is possible to change the colour and shape. This feature will allow, for instance, overlaying flux distributions in the metabolic layouts.CellDesigner SBML (CD-SBML): a graphical notation system proposed by Kitano [y Kitano , where leXtensible Graph Markup and Modeling Language (XGMML): a format based on the Graph Modelling Language (GML), being used for graph description using XML tags to describe nodes and edges of a graph. It is used, for instance, by Cytoscape.KEGG Markup Language (KGML): an exchange format created for the automatic drawing of Kyoto encyclopaedia of genes and genomes (KEGG) [s (KEGG)  maps.Systems Biology Graphical Notation (SBGN): defines three visual languages: Process Description (PD), Entity Relationship (ER) and Activity Flow (AF). For the purpose of this work, which focuses on metabolism, support was only developed for the PD language, based on Kitano’s proposal used in CellDesigner’s graphical representation, using bipartite graphs.COBRA Layouts: maps developed for the COBRA Toolbox. There are, currently, several maps on this format for many of the models hosted in the BiGG knowledgebase (http://bigg.ucsd.edu). These can be used on different models that have similar pathways, with a correct mapping of the identifiers between the layout and the BiGG model.Pathway generation: It is possible to generate a layout by using a list of reactions from a GSMM. This can be done following two strategies: choosing a list of reactions or, in the case where the model has pathway information, building layouts with the reactions from a set of pathways.The input/output layer provides support for different input/output formats:OptFlux has the main goal of providing a connection between the GSMMs loaded into OptFlux, their phenotype simulation and optimization results, and the layouts from the visualization framework.The visualization plugin for Through the plugin’s operations, it is possible for the user to map the identifiers of the metabolic model with the identifiers of the reaction and metabolite nodes of the layout. There are two different mapping methods available: loading a two-column file with the explicit mapping or applying regular expressions to the identifiers in the model and/or the layout. Another available operation allows the importation of KGML layouts, which can be automatically downloaded from the KEGG site.The third operation allows the creation of layouts from reactions of a metabolic model, using the pathway layout generation feature described above. The generation of this type of layouts can be made by selecting a pathway from the model or by selecting a list of reactions manually. It is also possible to select an existing layout as a basis for the new layout. This will allow creating new layouts or adding new reactions to existing ones.Each model can have a list of layouts associated, being possible to navigate from one layout to another by clicking the elements of that list. If the user clicks a metabolite that is present in another layout from the list, the information panel will display access buttons for those layouts.The most desired functionality of the connection between a ME and a visualization tool, is the ability to visualize phenotype simulation results (mainly flux distributions) overlaid in the network. This allows using the visualization tool to better understand the organism’s metabolism and design changes that can improve it towards some defined aim.OptFlux, to an overlap object that is used in the visualization. In OptFlux, simulation results have two major elements of interest for the visualization: flux distributions and genetic conditions. A flux distribution contains the flux values for each reaction. To represent it, a conversion of identifiers is needed. It can happen that two or more fluxes are mapped to the same reaction node, and the methodology chosen was to sum all those values . In the end, all these flux values, now mapped by reaction node, are normalized and used to determine the thickness of the edges. Additionally, the labels of the reaction nodes are also changed, adding the numerical value of the flux after the reaction name.To allow this operation, there is a conversion from a simulation result in The genetic conditions of a simulation are defined as all genetic changes made to the organism for that specific simulation. It contains all knock-outs (reaction deletions), and under/over expressed reactions. For the visual representation, some node shapes and colours were adopted to highlight these affected reactions. As seen in Figure Another type of overlap was also developed to visualize the comparison of two phenotype simulation results. The methodology followed was similar to the simulation overlaps. The genetic conditions are represented using the same symbols, but the colours of the edges follow a different strategy. Each simulation will have a colour by default, for instance, simulation 1 will have the colour red, and simulation 2 will have the colour green. Then, according to the flux for each reaction in each simulation, the colours will vary. If the amount of flux is larger in simulation 1, the colours will vary in a gradient that spans from red to black (where black means that there is no difference in fluxes), and if the flux value in simulation 2 is greater, the colours will vary from green to black. This will allow the user to identify where flux paths differ in the simulations (pure colours) and where both share fluxes (darker colours). At the same time, for reversible reactions, the fluxes of the compared simulations can take different directions. In this case, edges will have the colour of the simulation that follows the direction they are pointing, also giving the user an easy way to understand where the simulations differ. The thickness of the edges is calculated using the mean of the flux values in both simulations. On top of this, some filters are also generated, where it is possible to hide zero value fluxes in a simulation.OptFlux also provides a plugin that calculates the set of Elementary Flux Modes (EFMs) of a model. EFMs are the set of all routes through the network that cannot be decomposed to simpler routes [r routes , while mThe visualization plugin can convert these flux distributions into an overlap, in a way similar to the one used for the phenotype simulation results. Considering that, in this case, the only information available is the set of flux distributions, only the thickness and labels of the edges are changed. A visual filter can be applied hiding the reactions with zero value fluxes, thus allowing the visualization of the reactions that are part of the EFM.Regarding customization, the plug-in allows for the configuration of the style of the visualization through the Preferences option in the Help menu. This allows to personalize the layouts, defining parameters such as the colour and shape of the nodes or the font, size and colour of the labels. Perhaps more importantly, it is also possible to define the content of the labels of reaction and metabolite nodes, choosing which attributes to include from the ones available in the model. An example and more details of this process are given in the OptFlux documentation and in the case study description available in the Additional file E. coli. The full description of the workflow and required materials for both case studies are provided as Additional file To best illustrate the main features of the proposed tool, two case studies will be used, focusing on succinic acid (this section) and glycine production (next section) with E. coli metabolic model iJR904 [Succinic acid is an important compound to industry that has been produced mainly by chemical processes. Recently, there has been an effort to use microbial fermentation processes with anaerobic bacteria  and optil iJR904  was usedhttp://bigg.ucsd.edu/). After some manual and automatic curation, using the tools offered by the visualization framework, a second version of the layout was created and exported in the XGMML format, fully mapped to the model. A set of knockouts was selected from optimization results obtained using OptFlux [For visualization purposes, a COBRA layout was loaded for this particular model from the BiGG Database  to improve the quality of the generated results.After loading the pathway layouts, a simulation comparison of the wild type and knock-out mutant was performed. Visualizing the overlap of that comparison, it is possible to understand how both flux distributions differ by analysing the colours of the edges. The reference flux distribution is the wild type, represented by the green colour, while the knock out solution will be coloured red. As explained above, the more similar both flux distributions are, the darker the resulting colours will be, ranging from black to the colour of the simulation with the higher value. Figure fprica synthesis. Both reactions can be used to recycle glycine, which means that both deletions are essential to the solution.The inactivation of Isocitrate lyase (R_ICL) and Phosphoenolpyruvate carboxylase (R_PPC), both present in the central metabolism , providing its integrated visualization with GSMMs. The general-purpose nature of the core layer of the visualization framework allows the easy development of such tools, providing a good basis for the extension of the proposed software also in other directions.OptFlux that can be downloaded and installed from the homepage given below. The site also includes documentation for the plugin in the form of a wiki.The described plugin is included in the base distribution of Software name: OptFlux - software for metabolic engineeringProject home page:http://www.optflux.orgSpecific wiki page for the plug-in (with help):http://darwin.di.uminho.pt/optfluxwiki/index.php/OptFlux3:METAVIZOperating system(s): Platform independentProgramming languages: JavaOther requirements: Java JRE 1.7.x , GLPK or CPLEXLicense: GNU-GPL, version 3More details:


Clostridium acetobutylicum has been used to produce butanol on an industrial scale through acetone-butanol-ethanol (ABE) fermentation. A genome-scale metabolic (GSM) model is a powerful tool for understanding the metabolic capacities of an organism and developing metabolic engineering strategies for strain development. The integration of stress-related specific transcriptomics information with the GSM model provides opportunities for elucidating the focal points of regulation.Clostridia are anaerobic Gram-positive Firmicutes containing broad and flexible systems for substrate utilization, which have been used successfully to produce a range of industrial compounds. In particular, C. acetobutylicum ATCC 824, iCac802. iCac802 spans 802 genes and includes 1,137 metabolites and 1,462 reactions, along with gene-protein-reaction associations. Both 13C-MFA and gene deletion data in the ABE fermentation pathway were used to test the predicted flux ranges allowed by the model. We also describe the CoreReg method, introduced in this paper, to integrate transcriptomic data and identify core sets of reactions that, when their flux was selectively restricted, reproduced flux and biomass-formation ranges seen under all regulatory constraints. CoreReg was used in response to butanol and butyrate stress to tighten bounds for 50 reactions within the iCac802 model. These bounds affected the flux of tens of reactions in core metabolism. The model, incorporating the regulatory restrictions from CoreReg under chemical stress, exhibited an approximate 70% reduction in biomass yield for most stress conditions.We describe here the construction and validation of a GSM model for The regulation placed on the model for the two stresses using CoreReg identified differences in the respective responses, including distinct core sets and the restriction of biomass production similar to experimental observations. Given the core sets predicted by the CoreReg method, remedial actions can be taken to counteract the effect of stress on metabolism. For less well-known systems, plausible regulatory loops can be suggested around the affected metabolic reactions, and the hypotheses can be tested experimentally.The online version of this article (doi:10.1186/s13068-014-0144-4) contains supplementary material, which is available to authorized users. Clostridium, anaerobic Gram-positive Firmicutes, contain broad and flexible systems for substrate utilization [Clostridium acetobutylicum has been the model organism for the production of butanol on an industrial scale through the acetone-butanol-ethanol (ABE) fermentation [The organisms of the genus and class lization . Their ilization . In partentation .ABE fermentation is biphasic in nature; the acidogenic, exponential growth phase is characterized by the production of butyric and acetic acids, while the solventogenic stationary phase is characterized by the production of the ABE solvents. Production of acids and the resulting drop in the culture pH during the acidogenic phase drives the transition towards solventogenesis ,2. TheseAn important asset for understanding the metabolic capacity of an organism and deciding on metabolic engineering interventions is a genome-scale metabolic (GSM) model . These mC. acetobutylicum [C. acetobutylicum produces butanol and byproducts such as acetate and butyrate. More recently, two GSM models of C. acetobutylicum ATCC 824 have been developed [, one-sixth of the number of genes coded on its genome). The Senger and Papoutsakis model [C. acetobutylicum. The tricarboxylic acid cycle (TCA cycle), known to operate in a non-cyclic bifurcated manner, was recently shown to use Re-citrate synthase to produce α-ketoglutarate via citrate [13C-metabolic flux analysis (13C-MFA) data that both α-ketoglutarate dehydrogenase (α-KGDH) and succinate dehydrogenase (SDH) are inactive during the acidogenic phase [One of the earliest metabolic reconstructions was, in fact, a model of utylicum . A smallutylicum . These eeveloped ,21. Thesis model . A largeis model . Howeveric phase . In contic phase . While GA number of approaches have been proposed to incorporate regulatory information into GSM models. Regulatory flux balance analysis (rFBA) introduces Boolean constraints for gene expression into flux balance analysis (FBA) by linking the regulators to their targets in an iterative fashion ,27. The C. acetobutylicum ATCC 824, iCac802, validation with experimental data. New reactions and pathways absent in earlier models include an updated TCA cycle, a completed fatty acid synthesis pathway, and additions to the purine, pyrimidine, and cobalamin biosynthetic pathways. The iCac802 model along with the corresponding GPRs and metabolite information is available as SBML and excel files in Additional files iCac802 and predict nexus points of regulation, that underlie cellular response to the physiological stressors butanol and butyrate [In this paper, we describe the construction of a second generation genome-scale reconstruction of butyrate .iCac802 for C. acetobutylicum ATCC 824 spans 802 genes and includes 1,137 metabolites participating in 1,462 reactions. All reactions present are elementally and charge balanced. GPR associations were determined from the available functional annotation information and homology predictions accounting for monofunctional proteins, multifunctional proteins, isozymes, and protein complexes. The model was curated to remove any thermodynamically infeasible cycles, as detailed in the iCac802 model statistics and those of all other published models for C. acetobutylicum are shown in Table iCac802 has 64% more genes and 84% more reactions than the McAnulty et al. model [iCac802 contains a citrate synthase leading to a partial and bifurcated TCA cycle , which  [et al. . The lat [et al.  as reactrvations  and iCac13C-metabolic flux analysis (13C-MFA) [13C-MFA data revealed that four reactions (pyruvate carboxylase (PC), fumarate hydratase (FH), pyridoxal phosphate synthase (PLPS), and alanine-glyoxylate (AGT)), which were originally removed to eliminate thermodynamically infeasible cycles, carried flux in the organism, and therefore, they were reinserted in the model. The cycles were instead eliminated by removing three alternate reactions , succinate dehydrogenase (SDH), and malate dehydrogenase (MDH)) and by modifying the directionality of two others: succinyl-coenzyme A synthetase (SCS) was made reversible, and aspartate ammonia-lyase (ASPA) was restricted to the production of fumarate from aspartate. Figure The model was extensively tested to ascertain that it is capable of replicating flux ranges and phenotypes that have been documented for the wild-type (WT) organism and its mutants. The model predicted flux ranges were compared with experimental flux values from 13C-MFA) . The 13C13C-MFA analysis [−1 h−1. FVA was performed while constraining the growth rate to the WT value of 0.32 h−1 for C. acetobutylicum grown in complex media [C. acetobutylicum was grown in defined media by Au et al. [13C-MFA data [−1. Upon reapplying FVA with the biomass yield constrained to 0.07 h−1  was performed on the core carbon metabolism reactions, and the flux ranges were compared to the values obtained by the analysis . These eex media . The comu et al. , exhibitu et al. . In addiMFA data  was coll13C-MFA data, the model’s responses to gene knockouts and varying environmental conditions were also tested. The model was used to analyze the effect of increasing the size of the NADH pool on the production of various acids and solvents. It has been shown experimentally that an increase in the level of NADH leads to a concomitant increase in butyrate, solvents, and hydrogen production  in C. acetobutylicum [iCac802 in order to test the impact of glycerol as a carbon source. The increased availability of reducing equivalents showed a similar affect, as having no redox constraint in the model by allowing for free interconversion between NAD + and NADH or NADP + and NADPH resulted in an increase in butyrate, solvents, and hydrogen production, as seen in Table The model was also queried with respect to the ability to co-utilize glycerol. Glycerol as a highly reduced carbon source (its degree of reduction is 4.67 compared to 4.0 for glucose) allows for the generation of more reducing equivalents which drive the production of butyrate and alcohols . While utylicum . It is iutylicum ,5. BasedC. acetobutylicum by forcing the transition from acidogenic to solventogenic fermentation . CO inhibits the hydrogenase arresting H2 production  were subsequently calculated by fixing both the growth rate and restricting the acids/solvents to the FVA calculated maximum and minimum values. Yield ranges were determined by evaluating the ratio of acids/solvents to the corresponding minimum nutrient flux. Mutants ∆ack and ∆ptb reduce (but do not eliminate) acetate and butyrate production by removing acetate kinase (ACK) and phosphotransbutyrylase (PTB) activities, respectively . Regulatory constraints on the iCac802 model were imposed using the transcriptomic data from Wang et al. [g et al.  in the fWhen regulation was imposed on the model, the biomass yield decreased by approximately 70% for all stress conditions except for the low-level butyrate stress, where the biomass yield was unaffected. For each one of the stress conditions we identify the reactions (core set) for which the application of regulatory constraints is sufficient to reproduce the flux ranges seen in the model when all regulatory constraints are imposed. Core sets of reactions were identified for each of the stress conditions by comparing flux bounds of the regulated model with the imposed regulatory constraints . The presence of this reaction can be related to the regulation of the DNA replication and repair mechanism which is initiated to protect the DNA from any damage owing to the oxidative stress component of the butyrate stress . Howeveret al.  have repet al. . This absol operon  [The addition of butyrate in the media leads to earlier onset of solventogenesis with higher butanol production ,48, whicfA-ctfB) ,5. The CC. acetobutylicum could provide superior insight into predicting phenotypes for the development of strains with higher tolerance to stressors and higher production of desired products. Thus, a more stress resilient strain of C. acetobutylicum may be engineered by improving these cellular functions.A GSM model is a powerful tool that serves as a framework to visualize the changes captured from transcriptomic or proteomic data at the global metabolic level. The strength of such a model relies on the inherent characteristic capabilities to predict phenotypes from genotype. The proposed CoreReg method managed to elucidate focal points of regulation (core sets) on metabolic pathways. The core sets represent likely nexus points of regulation under stress conditions, as they can broadly propagate the regulatory effect to the stress affected pathways. Interestingly, different stressors and levels elicited different metabolic responses, as also corroborated by the DNA microarray data. The prediction of phenotypes and the corresponding regulation that leads to the phenotype along with model performance can be greatly enhanced by the development of a whole cell model. This would include the integration of regulatory knowledge derived from gene expression, transcription factors and their binding sites, regulation, and post-transcriptional regulation in the form of small non-coding regulatory RNA (sRNA) into GSM models. With the recent reconstruction of a transcriptional regulatory network  and the C. acetobutylicum ATCC 824, iCac802, and the use of transcriptomic data to apply additional constraints on reaction flux bounds using the CoreReg method. These constraints were calculated for varying levels of butyrate and butanol stress and were used to identify core sets of reactions whose changes in flux values can explain broadly all observed changes in metabolism.In this paper we have described the creation of a second-generation genome-scale metabolic model for CoreReg was able to differentiate between the two stressors, with a larger restriction on biomass for butanol stress. The core sets for butanol stress contain reactions in arginine and amino acid metabolism, while the butyrate stress core sets contain reactions in arginine and pyrimidine metabolism. These results corroborate previous findings concerning the down-regulation of arginine metabolism and regulation of DNA replication under stress conditions. Given transcriptomic data for other stressors or environmental conditions, the CoreReg method can be used to predict both the metabolic response and candidate focal points of regulation in terms of core sets. If there exists an available mechanistic description of the regulation, a remedial action can be taken to counteract the effect of stress on metabolism . In cases where the regulation mechanism is less well known, CoreReg results could be used to design plausible regulatory loops around the affected metabolic reactions. These regulatory hypotheses can then be tested experimentally.iCac802 entailed the following processes: 1) identification of biotransformations using previous models and homology searches; 2) assembly of reaction sets into a genome-scale metabolic model and subsequent conversion into a computations-ready format; 3) identification and removal of thermodynamically infeasible cycles; and 4) evaluation and improvement of model performance when compared to in vivo growth phenotypes.The general principles of the metabolic model reconstruction process have been previously described -51. ConsC. acetobutylicum ATCC 824 [We began metabolic model reconstruction by parsing the existing genome-scale models for ATCC 824 -22 and tATCC 824 . We alsoATCC 824 , to parsATCC 824 . We examATCC 824 . All reaet al. [Model curation began with the removal of thermodynamically infeasible cycles present in the model. Flux variability analysis (FVA) was performed with no biomass constraints to identify unbounded reaction fluxes. The number of unbounded reactions was reduced by restricting the directionality of certain reactions using Model SEED’s calculated values of the reaction’s Gibbs free energy. If the entire range, including error, was more than 4 kcal/mol removed from zero, the reaction was restricted to the direction specified by the free energy . The metet al.  was thenet al. . During et al. .13C-metabolic flux analysis (13C-MFA) data.Of the cycles found, those involving only two reactions were examined first. These were composed of equivalent reactions, that is, reactions which both converted a given set of reactants to products or vice versa using the same co-factors, varying only in their directionality. One of the two identified equivalent reactions was subsequently removed based on a preponderance of literature or annotation information concerning its directionality. Cycles containing more than two reactions were formed due to the presence of pathways that recycled metabolites consumed or produced by an alternate route with a zero net metabolic cost. Reactions in these cycles were reviewed, and those with no literature or annotation reference were either removed or had their directionality restricted. Figure After reviewing all of the cycles in the null basis with up to five participating reactions, the null basis was reevaluated. After fixing the smaller cycles, the same review process was extended to larger cycles. This reevaluation process was iterated until no more cycles were detected using FVA. A total of 101 reactions were removed from the model, and 58 had their directionality restricted to stop the involvement of 404 reactions in thermodynamically infeasible cycles.Flux balance analysis (FBA) was performed to obtain the maximum attainable growth rate under the given constraints .\documenSij is the stoichiometric coefficient for metabolite i in reaction j. vj represents the flux of reaction j, while j. N and M represent the overall sets of metabolites and reactions, respectively.where FVA was used to identify reactions present in thermodynamically infeasible cycles.No constraints were placed on the biomass in order to identify all thermodynamically infeasible cycles. This analysis was performed iteratively for all metabolites.13C flux data [in vivo gene knockout data from the literature [The model predictions were tested against experimental lux data , experimlux data ,38,40,41terature ,43,45,57While the acidogenic phase was simulated in the model solely through the inclusion of required nutrients, additional constraints were required for the solventogenic phase. The solventogenic phase of Clostridia is characterized by the uptake of acetate and butyrate along with the reduction of carbon flux towards amino acids . Thus, tet al. [Regulation was incorporated into the model by a stepwise procedure that modified the minimum and maximum flux bounds of reactions based on fold change values of corresponding gene expression values by a new method called CoreReg. Gene expression data for each stress condition (GSE48031 and GSE48039), obtained from Wang et al. . TranscrStep 1: FVA is performed on the unregulated (UR) model to obtain lower Step 2: FVA upper and lower bounds for the unregulated model are multiplied by the fold change value (cj) obtained using the transcriptomic data. The lower R) model are evaluated as follows:Note that the updated lower bound is non-zero only for reversible reactions, effectively lowering the maximum possible flux value in the reverse direction.Step 3: FBA is performed on the unregulated and the regulated model to obtain maximum biomass yields Step 4: FVA is performed at max biomass R) model to obtain lower Step 5: Reactions j whose flux bounds are equal to the regulatory constraints  for the previously determined k core sets are set to one, thus removing their regulatory role in the model. The process is repeated from Step 2 with the value of k increased by one.


Genetic and metabolic analyses of Escherichia coli strains showed that overexpression of PanB leads to accumulation of the likely folate cleavage product 6-hydroxymethylpterin and other pterins in cells and medium, and—unexpectedly—to a 46% increase in total folate content. In silico modeling of the folate biosynthesis pathway showed that these observations are consistent with the in vivo cleavage of 5,10-methylene-THF by a side-activity of PanB, with FolK-mediated recycling of the pterin cleavage product, and with regulation of folate biosynthesis by folates or their damage products.Tetrahydrofolate (THF) and its one-carbon derivatives, collectively termed folates, are essential cofactors, but are inherently unstable. While it is clear that chemical oxidation can cleave folates or damage their pterin precursors, very little is known about enzymatic damage to these molecules or about whether the folate biosynthesis pathway responds adaptively to damage to its end-products. The presence of a duplication of the gene encoding the folate biosynthesis enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (FolK) in many sequenced bacterial genomes combined with a strong chromosomal clustering of the  Mammals require a source of THF in the diet but plants and most microbes make THF de novo. Although many variations in the THF biosynthesis pathway have recently been discovered  by the C9–N10 bond, makes them inherently unstable. Folates are sensitive at physiological pH to oxidative or photooxidative scission to release the pterin and p-aminobenzoylglutamate (pABA-Glu) moieties , or 6-hydroxymethyldihydropterin (H2-HMPterin), whose side chains are oxidatively labile in vitro  have been detected in various bacteria and are sometimes secreted in large amounts  as a side-reaction, (ii) that cells repair this damage via the folate biosynthesis enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (FolK), and (iii) that folate biosynthesis is upregulated in response to PanB-inflicted damage.We present here comparative genomic, genetic, and metabolic modeling evidence that (i) the pantothenate (vitamin B5) biosynthesis enzyme ketopantoate hydroxymethyltransferase (PanB) cleaves 5,10-methylenetetrahydrofolate (CHhttp://www.ncbi.nlm.nih.gov/) were routinely used. Sequences were aligned using Clustal Omega  . Physical clustering was analyzed with the SEED subsystem coloring tool or the SeedViewer Compare Regions tool    Edgar,  on the c) Edgar,  using Ma) Edgar, . The phyE. coli strains used in this study included MG1655 (Coli Genetic Stock Center), BW25113  was routinely used for cloning.Bacteria were grown at 37°C on Luria Bertani (LB) medium (BD Diagnostics Systems) or on M9 minimal medium  was obtained from the ASKA collection of E. coli clones  with sulfathiazole (0–1 μg/ml) or trimethoprim (0–1.5 μg/ml). Plates were incubated at 37°C overnight. To test the effect of ΔpanB on sensitivity to folate inhibitors, the same assay was performed with wild-type BW25113 and BW25113 ΔpanB::kan with the exception that chloramphenicol was not added to the media and all minimal media contained 1 μM pantothenate.Sensitivity to antifolates was also measured by dilution drops onto various concentrations of antibiotic. Cultures were grown in 5 ml M9-glucose medium with chloramphenicol overnight at 37°C with shaking. The following day, the strains were diluted 1:20 in fresh M9-glucose medium and grown at 37°C with shaking until the cultures reached approximately AfolB, folE, folK, and panB were analyzed in MG1655 harboring either empty vector pBAD33 or the panB overexpression plasmid pCA24N::panB. Three biological replicates of each were grown overnight in M9-glucose medium with chloramphenicol at 37°C with shaking. The following day the cultures were diluted 1:100 in fresh M9-glucose medium with chloramphenicol and grown at 37°C with shaking. IPTG was added to 0.2 mM when the culture was at A600 0.2 and the induced cultures were harvested at A6001.0. RNA was extracted from each culture with the QIAGEN RNeasy Protect Bacteria Mini Kit, the concentration was determined by NanoDrop spectrophotometer, and RNA was stored at −80°C. cDNA was synthesized from 300 ng RNA using the iScript Select cDNA synthesis kit (Bio-Rad) using the provided random primer mix. Quantitative PCR was performed using the MyiQ2 Real Time PCR Detection System (Bio-Rad) using iTaq Universal SYBR Green Supermix (Bio-Rad). Amplification parameters were 95°C for 3 min followed by 40 cycles of 95°C for 10 s, 59°C for 30 s with fluorescence measurement, followed by the establishment of a melting curve. Data were analyzed with the IQ5 software (Bio-Rad) and the Bio-Rad Expression Macro. Expression was normalized against two reference genes: rssA (b1234) and rpoA (b3295). All primers used for the RT-PCR are listed in Table Expression levels of folK1) and ACIAD2407 (folK2) were PCR-amplified with primers ACIAD3062-xbaI-5 (5′-CTA CTCTAGAATGAGCATAACCACCTATAT CG-3′) and ACIAD3062-SalI-3 (5′-CATTGTCGACCGCGT TATTTTTCAACCCAG-3′) and ACIAD2407-xbaI-5 (5′-CAT TTCTAGATTGAACGCCAACGCCACAATTTT TG-3′) and ACIAD2407-SalI-3 (5′-CAATGTCGACGAATT ATGATGAAGAAATCAC-3′), respectively. Acinetobacter baylyi ADP1 genomic DNA was used as the template for PCR. PCR products were digested with XbaI and SalI, purified with the Zymo Clean and Concentrator-5 kit, and ligated into XbaI/SalI-digested pBAD24. The ligation mixtures were used to transform E. coli GC10 and transformants were selected on LB with ampicillin. pBAD24::folK1 and pBAD24::folK2 were confirmed by sequencing and the plasmids were renamed pJJT115 and pJJT107, respectively.ACIAD3062  or dT. If the folK gene on the plasmid complements the ΔfolK, the colonies appear after overnight growth at 37°C on LB with ampicillin and arabinose without dT.pJJT115, pJJT107, or pBAD24 were transformed via electroporation into panB expression plasmid was constructed as follows. The panB gene was amplified from genomic DNA of strain W3110 by PCR using primers EcPanBp19Fwd (5′-CTA GAAGCTTATGACAGGAAACAGCTATGAAACCGACCACCATCT C-3′) and EcPanBp19Rev (5′-GATCGAATTCTTAATGGA AAC-TGTGTTCTTCG-3′), and cloned into the HindIII and EcoRI sites of pUC19  were grown on M9 glucose (0.4%) and 10 μM pantothenate. Cells were harvested when A600 reached 1.0. For panB overexpression analyses, the strains (wild type MG1655 harboring the vector pUC19 or containing panB) were grown on M9 glucose (0.4%) with added Amp. IPTG (0.5 mM) was added at A600 of 0.3. Three independent colonies for each were cultivated. Only the cultures overexpressing panB had filaments (cell lysis) after adding IPTG (repeated twice independently). Cells were harvested when A600 reached 1.0. Protein contents of harvested bacterial cells were determined using the Pierce bicinchoninic acid (BCA) assay kit. Pterins were extracted, converted to their oxidized forms, and analyzed by HPLC with fluorometric detection as described , and the proposed PanB side reaction, the model included exchange reactions that simulate the production of H2-HMPt and pABA by reactions outside the selected scope of the model. Similarly, exchange reactions were added to simulate the continuous dilution of THF and CH2-THF that occurs during cell growth . Increasing the kinetic constant in the mass-action kinetic equation will increase the instantaneous flux of the associated reaction, but then the substrates of the reaction are consumed faster than they are produced, causing a decline in substrate concentration, and restoring flux to its original steady-state value. In this case, the steady-state flux through the Fol[KPCA] reactions will be the flux entering the pathway via the Hvmax values exceed the net steady-state flux that these reactions must achieve (vnet + vPanB).The model was also insensitive to the saturation state of the FolK, FolP, FolC, FolA, and PanB reactions. All of these reactions were modeled as completely unsaturated reactions, essentially following mass action kinetics. We chose mass action kinetics for these reactions, as opposed to unsaturated Monod kinetics, because this reduces the number of parameters, simplifies the model, and produces equivalent behavior when the enzyme is in a completely unsaturated state. However, we did determine that modeling these reactions as saturated enzymatic reactions results in similar behavior and steady states so long as the 2-THF. The ratio and magnitude of these rate constants dictated how close this reaction was to equilibrium, as well as what the equilibrium ratio of THF and CH2-THF would be. The total steady-state concentration of THF and CH2-THF was controlled by the value of vnet and the kinetic parameters on the drain reactions for THF and CH2-THF. The THF and CH2-THF drain reactions represent the consumption of these compounds during cell growth and dilution. Because the value of vnet was fixed, the only adjustable parameters governing the total THF and CH2-THF concentration were the kinetic parameters on the drain reactions. These parameters were adjusted to ensure that the total concentration of THF and CH2-THF predicted by the model matched experimental data under all conditions studied. Given these constraints, these kinetic parameters were not flexible. Rather, only a single set of values could be found to produce the optimal fit to the experimental data.In contrast, the kinetic parameters on the GlyA reaction exercised a large degree of control over the ratio of steady-state concentrations for THF and CH2-HMPt, as well as the magnitude of the recycle flux back to H2-HMPt. This flux controls the dynamic response of the folate pathway intermediates, including the initial dip that occurs in the H2-HMPt concentration immediately following the induction of the PanB enzyme, which we have proposed as the cause of the overall induction of the folate pathway. We tuned the kinetic parameters on the PanB reaction in our model to fit the experimentally measured concentrations for H2-HMPt. We currently model this reaction as unsaturated following irreversible mass action kinetics, but behavior would be similar if the reaction followed saturated Monod kinetics.The other key parameters in the model are the kinetic constants on the PanB reaction, which control the steady state concentration of HfolK). This observation had already been made when the subsystem was first constructed with far fewer genomes  and 18% harbor a single folK gene that clusters with panB   a single folK gene clusters with both panB and folB  in plants and yeast  Figure . FurtherB Figure . To elimB Figure . Very siB Figure . These aB Figure . The sepfolK, both have 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase activity in vivo, the folK1 and folK2 genes of A. baylyi ADP1 were tested for the capacity to complement the dT auxotrophy a ΔfolK strain of E. coli. The folK homolog found next to panB  robustly complemented the dT auxotrophy, whereas the one next to folB  did not .In order to test whether, from genomes with two copies of t Figure . This fiB Figure . This wapanB gene encodes the CH2-THF-dependent enzyme ketopantoate hydroxymethyltransferase (EC 2.1.2.11). This suggested an explanation for the observed association between panB and folK based on the proposed reaction mechanism of PanB. Powers, Snell, and coworkers first purified this enzyme and showed that it is a class II aldolase  . In path A, the other reaction product is 2-dehydropantoate; in path B, α-ketoisovalerate is regenerated along with an unstable bis-hydroxymethylpterin, which spontaneously loses formaldehyde to give H4-HMPterin. The H4-HMPterin formed by either path could re-enter the folate pathway via FolK after spontaneous oxidation to the dihydro form  and trimethoprim (a dihydrofolate reductase inhibitor).If a side-reaction of PanB cleaves CHF Figure , then ovpanB was tested by transforming either E. coli strain BW25113 or MG1655 with the ASKA clone expressing panB under control of the lac promoter (ppanB) or with an empty vector (pBAD33) control. Sensitivity to trimethoprim and sulfathiazole was assessed for each strain by measuring the halos of inhibition of different concentrations of each drug. The strains overexpressing panB were more sensitive to both trimethoprim and sulfathiazole resulting in larger zones of inhibition .To assess whether deleting 6 damage that propagates to CoA and folate metabolism .Growth phenotypes can be caused by very indirect effects, as shown in recent studies on mutants affected in vitamin BpanB (as a pUC19 construct) in E. coli MG1655 indeed led to accumulation of 6-hydroxymethylpterin in both medium (five-fold) and cells (three-fold)  Figure . Also, tl Figure . The rats Figure . Note ths Figure .panB. As shown in Figure 2-THF  that were partially offset by decreases in 5-formyl-THF and 5,10-methenyl-THF/10-formyl-THF . The folate pools that increased were largely polyglutamyl forms . Upon IPTG induction, the expression of panB increased over E. coli MG1655 harboring empty vector by up to 6000-fold. When panB induction was 6000-fold, the expression of folK, folB, and folE increased by about 10-fold , however, the expression of all three folate genes was essentially unaffected (not shown). Variation in induction of panB presumably reflects the stochastic nature of induction, as documented for the lac promoter both experimentally and through modeling . This is consistent with the kinetic and thermodynamic data available for these reactions . While measured values are not available for many of the metabolite concentrations and kinetic parameters in the model, these parameters are restricted by the need to replicate experimental observations. Once complete, we simulated the model under wild-type conditions, demonstrating that the steady-state predicted by the model was consistent with all the experimental observations.Kinetic parameters and metabolite concentrations were selected for the model to fit physiological conditions and replicate the wild-type concentrations measured for HF Figure . The mod2-THF (and THF) concentration began to drop due to the larger flux through the PanB side reaction. This led to a rise in the concentrations of H2-HMPt , which in turn led to a rise in the flux through the THF synthesis pathway, leading to the slow recovery of the THF concentration back to—but not exceeding—the wild-type values. Thus, this simulation successfully replicates the rise in H2-HMPt concentration that accompanied the overexpression of PanB in our experiments, but it fails to replicate the rise in THF concentrations, meaning the overexpression of PanB alone cannot explain all experimental observations.Next, we simulated the overexpression of PanB by increasing only the kinetic constant of the mass-action kinetic equation for the PanB folate-cleaving reaction (which integrates the enzyme concentration of PanB), leaving all other model parameters the same. In this simulation, all metabolite concentrations started at the steady-state values predicted from the wild-type model Figure . Immedia2-HMPt and pABA at the same time as we increase the kinetic constant of the mass-action kinetic equation for PanB kinetic constant. In this scenario, we still see an initial dip in THF concentrations, which accompanies the rise in H2-HMPt, but this time, the THF concentrations recover more rapidly and ultimately rise beyond the wild-type levels and reach new steady-state values that closely resemble those observed in the PanB overexpression experiments  was almost ten-fold less than the increase in pterin production (4.7 nmol mg−1 protein), all of it found in the medium. Thus, an increase in intracellular folate cleavage triggers a doubling of pterin production, most of which flows not to folate synthesis but out into the medium.Overexpression of PanB caused expected and unexpected effects. Expectedly, levels of 6-hydroxymethylpterin and total pterins increased. Unexpectedly, so did folate levels. However, as kinetic modeling showed, the folate increase can be accounted for by a very reasonable assumption, viz. that depletion of certain folates (or conceivably the buildup of folate damage products) leads to upregulation of the folate pathway. he observed increase in folate production appears to be the only case so far reported of a folate pathway regulatory response to a physiological perturbation  grants MCB-1153413.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.