We present Redirector, a new Flux Balance Analysis-based framework for identifying engineering targets to optimize metabolite production in complex pathways. Previous optimization frameworks have modeled metabolic alterations as directly controlling fluxes by setting particular flux bounds. Redirector develops a more biologically relevant approach, modeling metabolic alterations as changes in the balance of metabolic objectives in the system. This framework iteratively selects enzyme targets, adds the associated reaction fluxes to the metabolic objective, thereby incentivizing flux towards the production of a metabolite of interest. These adjustments to the objective act in competition with cellular growth and represent up-regulation and down-regulation of enzyme mediated reactions. Using the iAF1260 E. coli metabolic network model for optimization of fatty acid production as a test case, Redirector generates designs with as many as 39 simultaneous and 111 unique engineering targets. These designs discover proven in vivo targets, novel supporting pathways and relevant interdependencies, many of which cannot be predicted by other methods. Redirector is available as open and free software, scalable to computational resources, and powerful enough to find all known enzyme targets for fatty acid production.Advances in computational metabolic optimization are required to realize the full potential of new  A deeper understanding of biological processes, along with methods in synthetic biology, is driving the frontier of metabolic engineering. In particular, a better representation of cell metabolism will enable the engineering of bacterial strains that can act as factories for valuable biochemical products, from medicines to biofuels. Models which predict the behavior of these complex biological systems enable better engineering design as well as a more comprehensive understanding of fundamental biological principles. Here we develop a new method, called Redirector, for modeling metabolic alterations, and their relationship to cell growth. This method optimizes genetic engineering changes to achieve metabolite production using a new representation of the metabolic impact of genetic manipulation, which is more biologically realistic than existing models. We discover proven and novel engineering targets to improve fatty acid production, correctly predicting how different combinations of genes build upon one another. This work demonstrates that Redirector is a powerful method for designing cell factories and improving our understanding of metabolic systems. Building a better predictive understanding of genome-scale metabolic networks is critical to fully harnessing the power of bacterial metabolism in general and for designing biofactories in particular. Biofactories have been engineered for a variety of products including pyruvate While kinetic models have been developed to simulate biological networks FBA has been used to successfully design production strains by optimizing metabolic alterations such as gene knockouts In vivo engineering and kinetic modeling have shown that engineering individual enzymes has a limited potential to change the flux through a metabolic pathway Representing genetic alterations to a metabolic system  as direct changes to flux boundaries presents a number of problems. Firstly, representing metabolic alterations in this way is difficult in the common case when a single enzyme affects many reactions. Imposing different flux bounds on reactions controlled by the same enzyme creates a disconnect with experimental implementation. However, applying the same flux constraints to all reactions controlled by one such enzyme will often fail to produce the desired metabolite. Second, using a limit on one flux is sufficient to control a whole pathway, and all up-stream reactions, in an FBA model. Further, multiple metabolic alterations will often only be as effective as the tightest limit imposed, and metabolic alterations beyond the single strongest will often provide no additional benefit. To address the above issues and in order for metabolic design optimization to reach its full potential, metabolic alterations must be represented in a more biologically relevant way. Hence, we develop a framework modeling metabolic alterations using the FBA objective to represent the balance of resource allocation between growth and metabolite production. Metabolic alterations (up- and down- regulations) are modeled through incentivizing flux changes by adding reaction fluxes to the existing FBA biomass objective with associated positive or negative coefficients. These coefficients determine the relative strengths and direction of the impact the metabolic alterations have on the reaction fluxes. We can then find a set of metabolic alterations optimized for the production of a metabolite of interest, using a bilevel optimization approach. To make this possible, we develop a method by which an optimal set of reactions, grouped by enzyme, can be included in, or excluded from, the metabolic (inner) objective. We maintain the original flux that makes up the biomass function, along with the added incentives on fluxes towards metabolite production in the inner FBA objective, to ensure that selected metabolic alterations toward metabolite production account for cellular growth.It is important to enable Redirector to discover a growing set of metabolic alterations that work synergistically to drive flux towards production to better overcome growth driven adaptation and regulatory mechanisms. To achieve this, we improve the iterative local search in GDLS In objective control  the inneBecause both the biomass and reactions leading to the production of a metabolite appear in the objective, if a high metabolite production level is achieved, discovery of new targets will only continue after increasing the incentive for growth in the objective. This process incentivizes resources to biomass and necessitates new metabolic alterations to meet the metabolite production goal, dictated by the outer objective of the bilevel optimization. For this reason, we have developed progressive target discovery. After each iteration of bilevel optimization using objective control, the Redirector algorithm checks if there have been new metabolic engineering targets discovered, and also checks the level of production of the metabolite for which we are optimizing. n,−2n) where n≤0, and the sensitivity library is created by performing sensitivity analysis for every reaction on each of the growth and production objectives. The flat library is the simplest approach, giving each reaction equal weight but not allowing further tuning of the targets. The power series library allows for tuning the impact of metabolic targets but is computationally intensive. Finally, the sensitivity library indicates how a reaction flux influences the metabolite production or growth, with only those reactions that directly affect one of these objectives getting a coefficient. Thus, using the sensitivity redirection coefficient leads to a smaller pool of enzymes from which to select targets, and therefore, a less computationally intensive optimization.The optimal set of targets to drive metabolite production is in large part determined by their relative weighting in the objective. Reaction fluxes are included in the objective using weights, called redirection coefficients (β), selected from a set of values we call the redirection coefficient library. In this work we focus on three methods we have developed for constructing the coefficient library which we term the flat, power series and sensitivity redirection coefficient libraries , using the iAF1260 genome-scale k) were run to 10 iterations optimizing for myristoyl-CoA. Here we allow no tuning of the level of metabolic alteration (tuning of the redirection coefficients and the associated parameter (s) are discussed in the Supporting Information To provide insight into the progress of design construction using the Redirector Framework, we present k = 4 and k = 5 do not progress beyond iteration 3 and 6 respectively, indicating that no more solutions were found in the allotted search times beyond this point. We observe that searching with different neighborhood sizes allows us to discover designs that overcome locally optimal solutions and the challenging nature of MILP optimizations. Preselecting the redirector coefficient library with a sensitivity analysis improves search performance as indicated by To give an overview of the performance of the Redirector method we present k = 6. This design achieved one of the highest levels of the progressive growth parameter and has 20 simultaneously active targets. Most of the enzyme targets found fall into one of 4 pathways: pentose phosphate, glycolysis, fatty acid degradation or fatty acid biosynthesis. The network in To show an illustrative example of a Redirector design, we optimize for the production of myristoyl-CoA, and chose the design from the optimization results found after 15 iterations using the largest search size rpiAB and tktAB) act to produce NADPH, which is needed for fatty acid production, as well as drive flux towards D-glyceraldehyde-3-phosphate. The overproduced D-glyceraldehyde-3-phosphate from the pentose phosphate pathway leads directly into glycolysis, indicating a direct link between the engineering changes in the two pathways. In glycolysis  drive carbon flux towards pyruvate and acetyl-CoA. Up-regulation of both pgk and gpmAM is an example of the Redirector framework's ability to discover multiple targets in a non-branching, linear pathway in the iAF1260 model. Up-regulating pgk increases production of 1,3-bisphospho-D-glycerate, which is only used in the reaction catalyzed by gpmAM. As mentioned previously finding multiple simultaneous targets in a linear pathway is a proven engineering strategy and would not be found if metabolic alterations are modeled using flux boundaries.In ycolysis  the up-raccABCD, fabD and (fabB or fabF) pulling flux from acetyl-CoA and towards fatty acid production. We also find intuitively rational targets for fatty acid biosynthesis including up-regulation of (fabB or fabF), fabG, and (fabA or fabZ), and discover proven fatty acid production targets, such as up-regulation of fadD as well as the knockout of fadE. While the enzyme group (fabB or fabF) is increased, fabB alone is decreased in this design. This seeming contradiction is a function of working with enzyme targets since (fabB or fabF) is recognized as one enzyme group that controls one set of reactions while fabB alone is recognized as a separate enzyme in the iAF1260 E. coli model. A simple way to implement this would be to up-regulate fabF while down-regulating fabB. In addition to these targets in closely linked pathways, we discover two targets, folD (formylTHF biosynthesis) and idi (isoprenoid biosynthesis) (nthesis) , that arfabA or fabZ), fabG and (fabB or fabF) works to drive flux though the whole of fatty acid biosynthesis, 12 reactions for each enzyme. In the final optimization design each of these enzymes has been increased to one level, incentivizing all the associated reactions. We compare the final set of flux values resulting from this Redirector optimization to fluxes resulting from the optimization for biomass. This analysis indicates that only the fluxes through 6 reactions upstream of myristoyl-ACP increase, while the fluxes through 3 reactions for biosynthesis of larger unsaturated fatty acids do not change, and the fluxes through 3 reactions producing unsaturated fatty acids actually decrease.The metabolic engineering targets shown in tesA, fatty acids are redirected from biomass and converted to free fatty acids fadD enzyme then catalyzes reactions leading to the addition of the Coenzyme A to the C14:0 free fatty acid. Both fadD and tesA are up-regulation targets found in separate optimizations and, along with knockouts interrupting the β-oxidation of fatty acids (ΔfadE), ensure that myristoyl-CoA is overproduced while no product with chain length larger than myristoyl-CoA will be produced in excess. This result matches with experimental analysis showing that the combination of these metabolic engineering targets result in the preferred production of C14 fatty alcohol Fluxes through the longer chain fatty acids, bigger than C14:0, do not increase, as we have added an export reaction for myristoyl-CoA into the model, such that myristoyl-CoA can be exported when it is overproduced. This selectivity for the carbon chain size of fatty acids and biofuel product export is biologically relevant. It has been shown that, with up-regulation of fadD only 1 shows up-regulation. An optimization for myristoyl-CoA using a method that directly changes flux bounds, in the same manner, for every reaction catalyzed by an enzyme would prove difficult. For example, increasing the flux bounds for every reaction mediated by any of the fatty acid biosynthesis enzymes , would cause some of these reactions to draw flux away from the intended product.E. coli, where knocking out fadE has no effect on fatty alcohol production unless fadD and tesA′ have been up-regulated first The order in which genetic manipulations should be targeted is important information since the efficacy of some genetic alterations can depend on other genetic changes being made beforehand. Genetic manipulation is often carried out serially with a selection, and if there is an order of efficacy for these targets it is important to understand that order for the selection to work. This effect is illustrated when trying to produce fatty alcohols in accABCD, (fabA or fabZ), (fabB or fabF), , (fadK or fadD), fabG and , as well as decreasing fatty acid degradation by reducing fadE and (fadA or fadI). The pentose phosphate pathway is enhanced through the up-regulation of tktAB, pgl, pgk and  which drives flux towards acetyl-CoA. The TCA cycle is generally repressed via the reduction of acnAB, icd, , (sdhABCD) and gltA. The down-regulation of fre results in the presence of more NADH and NADPH, which are used in the fatty acid biosynthesis cycle. The down-regulation of serA acts to halt animo-acid pathways from drawing flux from the pentose phosphate pathway, in particular 3-phospho-D-glycerate which is the direct product of the pgk enzyme.icd, pgk, and trpC. The trpC enzyme is part of the L-tryptophan synthesis pathway and icd is part of the TCA cycle, both of which direct resources away from fatty acid synthesis. The combination of trpC and pgk is not found by the flat coefficients and may be a result of a finely tuned balance of forces from the sensitivity redirection coefficient library. The sensitivity redirection coefficient library dependency targets, while sparser, also center on fatty acid biosynthesis and degradation targets with the exception of gltA,  and acnAB group and the pgk and trpC group. The pgk and trpC group also combines with two new targets pssA and psd. Both are down-regulated and result in the repression of the lipid biosynthesis pathways which reduces the use of fatty acids for lipids.In order to give a more complete picture of the dependency sets we present We further illustrate the importance of the Redirector approach, using objective control, by contrasting it with the limitations of using flux boundaries to model metabolic alterations. Further details beyond those presented here are included in the Supporting Information This method proved to be problematic in two ways . First, The Redirector framework provides a new capability in modeling metabolic alterations, using the FBA objective. This capability is harnessed to develop designs incorporating many metabolic alterations, which work in concert to drive flux in new directions and result in high production cellular metabolic factories. The objective control approach provides a more biologically relevant model of metabolic alterations, avoiding the unrealistically unlimited impact of changing flux boundaries. The Redirector framework is able to successfully develop designs for pathways where multiple chemical reactions are catalyzed by single enzymes, such as those that have elongation cycles, or complex branching or alternative pathways such as fatty acid metabolism. These designs find experimentally proven combinations of engineering targets along with novel targets in intuitive as well as distant pathways. Analyzing orthogonal and overlapping designs discovered by the framework, target dependency network mapping elucidates the relative importance and relationships of metabolic targets, in order to guide metabolic engineering. All together these methods form an effective, flexible and widely applicable framework for developing metabolic engineering designs for high production strains.acc, fabA and fabD as well as reduction of fadE. Acetyl-CoA carboxylase (acc) catalyzes the first committed step toward fatty acid biosynthesis. Up-regulation of acc leads to an increase in overall fatty acids fabA, 3-hydroxydecanoyl-[acp] dehydrase, has been shown to increase the level of fatty acid metabolites present in the cell fadD while knocking out fadE, has been shown to result in biofuel production from acyl-CoA precursors To demonstrate its capacity to optimize challenging pathways, we have applied Redirector to the production of myristoyl-CoA, examining the highest growth parameter design as well as the dependency analysis of multiple designs. The single high growth parameter design rediscovers experimentally proven combinations of targets including up-regulation of fumABC, acs, sucAB, acnAB, glyA and sdhABCD as well as increasing aceEF, and pgkidi (isoprenoid biosynthesis) and folD (formylTHF biosynthesis), to reduce competition for carbon. Previous computational production designs have used folD knockouts to prevent flux away from 3-p-Glycerate towards formate idi has been shown to increase production of isoprenoids Looking at the single myristoyl-CoA design in acc, pgk, (aceEF and lpd), and reductions of acnAB, fumABC, as well as reduction of sucCD in an alternate design path. The only experimentally tested OptForce target not found by Redirector was reduction of mdh. However, this target makes little improvement on its own and seems to hurt production when combined with any of these other targets experimentally. Redirector also finds experimentally validated targets not found using the OptForce approach, including the reduction of glyA (glycine production) and fatty acid biosynthesis initiation (fabBF) as well as reduction of sdhABCD (TCA cycle) in the dependency network mapping (Supporting Information acc and bpl), individual knockouts of sdhABCD or glyA result in an additional ∼200% or ∼300% (mg/L/OD) respective increase in naringenin production Using objective control, Redirector pushes fluxes in new directions finding ever higher impact metabolic engineering designs. Alternatively, OptForce, a method with similar goals as Redirector, iteratively constrains the system to find minimal sets of reactions that force more flux into the desired product. We have shown that using flux bounds based models of metabolic alterations proves challenging for fatty acid production for three main reasons. First, if flux bounds are not sufficiently strict, no viable constraint sets will be found. Second, the flux bounds discovered can lead to unrealistic constraints when mapping reactions to causal enzymes. Third, limits do not work additively which restricts the number of targets that can work together in any one design, causing experimentally proven targets for fatty acid production to be missed. To further compare these methods, we applied the Redirector framework to the production of malonyl-CoA, which has been optimized as a precursor for the production of the flavonoid naringenin using OptForce accABCD and down-regulation of fatty acid biosynthesis initiation . These targets exclusively make up the size 2 dependency sets and participate in most size 3 dependency sets. The importance of these two groups is quite intuitive as accABCD directly produces malonyl-CoA while fatty acid biosynthesis draws directly from malonyl-CoA. The primacy of these targets is confirmed in successful metabolic engineering strategies. Overexpression of acetyl-CoA carboxylase, or repression of fatty acid biosynthesis initiation have been sufficient to increase naringenin production 2 to 3 fold accABCD can be enhanced but not replaced by overexpression of targets upstream of acetyl-CoA. This interdependency is in direct agreement with experimental evidence. Comparing dependency network mapping to experiment demonstrates that the Redirector method discovers realistic, minimal sets of core targets and the manner in which further targets can build on this core.The breadth of malonyl-CoA production target combinations also allows us to further compare our dependency network mapping to experimental results for engineering target interdependencies, elucidating those targets which are required for others to be effective. Looking at the target dependency network mapping  described in the Supporting Information The Redirector framework selects the optimal enzymes and metabolic changes and includes the related reaction fluxes in the redirection function by choosing from a list of possible redirector coefficients as set out in the redirection coefficient library. The inclusion of a positive redirection coefficient for a flux in the redirection function incentivizes increase of that flux  and a negative redirection coefficient has the opposite effect. Discovery of the optimal magnitude of redirection coefficients informs the relative strength of metabolic engineering changes. The optimal set of enzyme targets is determined as much by the reactions affected, as it is by the possible redirection coefficients in the redirection coefficient library. Further details of these redirection coefficient libraries can be found in the Supporting Information We extend the bilevel implementation of objective control to find progressively higher impact sets of interacting targets. This is achieved by harnessing the competition between the two parts of the system objective, in which the growth function directs resources to the biomass, while the redirection function directs resources to the metabolite production. Once an optimal set of metabolite production targets has been discovered and the production objective is at its optimal possible level, no more targets will need to be discovered. However, increasing the relative strength of the growth function will necessitate selecting more enzyme targets to once again achieve high metabolite production. To this end, we expand the iterative local search method to include the adjustment of the progressive growth parameter (γ). At each iteration, γ is increased to a value where more targets must be selected to increase the strength of the redirection function and satisfy the production objective. This allows the Redirector framework to build upon the set of enzyme targets at each iteration. The combined effect of these targets results in ever increasing set of incentives to drive flux towards the production objective until the maximum potential redirection function is reached.new, that will result in an effective growth function value which is at least slightly larger than the contribution of the current redirection function to the system objective. The first term in the equation is the current strength of the redirection function. This term is calculated as the included redirection coefficients βjl multiplied by the difference in current flux vj and the flux when growth is maximized vjmax growth, for each included reaction j. The variable δprogress is a small number used to insure γnew is slightly larger than the current strength of the redirection function. This new progressive growth parameter will increase the effective strength of the growth function in the system objective such that overcoming it requires the inclusion of new reaction fluxes in the redirection function as a result of new enzyme targets being selected. The logical flow of the Redirector iterative search local algorithm, which incorporates the progressive growth parameter, is detailed in progress and γ parameters in Supporting Information To drive the discovery of new targets we seek to increase the value of the progressive growth parameter (γ) such that the growth term will dominate the system objective. This is achieved by finding a new value of the progressive growth parameter, γMany enzyme targets generated during the progressive target discovery depend on the inclusion of other core targets before they can contribute to an increase in the production objective. To determine the order in which targets should be engineered as well as their interdependency we develop a dependency network mapping method.To carry out the process of dependency network mapping all targets for one production objective from separate neighborhood sizes and redirection coefficient libraries are pooled in any relevant combination. Then all subsets of this target pool up to size N are searched in separate optimizations, by forming the relevant system objective and performing a single-level FBA with this objective. The resulting flux states are checked to discover if the target combinations result in at least 20 percent of the maximum possible production of the metabolite of interest and, importantly, if they result in higher production than their component target sets. Through this analysis we discover which targets work as singles, doubles etc. In this way, dependency network mapping shows which enzymes form the core of metabolic production designs. Currently we focus our dependency network mapping on the discovery of dependency target sets needed to produce the metabolic product when γ = 0.02; thus, we only require that each engineering design needs to overcome a very weak growth function. As a result, the large sets of simultaneous targets found in progressive growth driven target discovery, which require larger values of γ, are not rediscovered.https://github.com//bionomicron/Redirector.git.The Redirector framework is built using free, and whenever possible, open software in a flexible lightweight solution. The core is built with Python and currently uses the GLPK and SCIP solvers. LP optimizations were largely carried out in GLPK because of the ability to directly access GLPK functions from Python while MILP optimizations are carried out by SCIP for faster solving speed. Computation was carried out on the Broad Institute computational cluster. The Redirector Package including operational software code and metabolic network model files used for this publication are available at Figure S1Myristoyl-CoA optimization search time. Search time in seconds vs. the iteration number for the optimization of myristoyl-CoA. The color of the lines indicates associated neighborhood size. A. Search time vs. iteration for myristoyl-CoA using the flat adjustment library. B. Search time vs. iteration for myristoyl-CoA using the sensitivity adjustment library.(EPS)Click here for additional data file.Figure S2Fatty acid concentration in strains with metabolic alterations. Relative fatty acid concentration, as measured with the Roche Free fatty acids, Half-micro test, in four different strains of E. coli with varying levels of anhydrotetracycline (ATc) induction. The blue bar represents EcfC1, a λ-red recombination strain, the green bar represents EcfC1 with fadE gene knocked out, the red bars represent EcfC1 with the fadE knockout and tesA′ and fadD overexpressed with ATc induction, and the dark brown bars represent EcfC1 with the fadE knockout as well as tesA′, fadD and fadR overexpressed with ATc induction. Gene expression was induced with 0, 3, 5, and 8 ng/ml ATc.(EPS)Click here for additional data file.Table S1Malonyl-CoA optimization results. List of targets from an optimization of malonyl-CoA at neighborhood size 3 and iteration 5. A. Optimization design results for the flat redirection coefficient. B. Optimization design results for the power series redirection coefficient. Total Flux Change represents the summation of all flux changes to the reactions that the enzyme controls. Flux Change Count gives an overview of how the fluxes, associated with each enzyme, change as a result of this design. Change is calculated by comparing the value of the flux at current optimal system objective to those found during optimal growth. We indicate the number of reactions with flux levels that decrease (−), stay the same (no change), or increase (+).(DOCX)Click here for additional data file.Table S2Malonyl-CoA dependency network. The double and triple metabolic alteration target dependency groups found for malonyl-CoA production are shown along with the predicted amount of production. There were no single enzymes that were found by the dependency analysis. Production indicates the amount of malonyl-CoA made by that dependency group.(XLSX)Click here for additional data file.Table S3Variable summary. This table gives an overview of the variables used in the Redirector method. The variable name, a basic description of the purpose of the variable, and how the value of the variable is determined are presented. The dependent variables of the bilevel optimization  are determined by solving the optimization problem.(DOCX)Click here for additional data file.Table S4Progressive target discovery robustness. This table illustrates the robustness of the Redirector method specifically the progressive target discovery to varying values of δprogress. Shown here are the targets discovered by the Redirector method for the production of myristoyl-CoA (C14:0-CoA), using a search size of 4 metabolic alterations (k = 4) during iteration 3 and 4 . The left most column indicates the gene id of the targets. Redirection coefficients for the selected targets and the sum of fluxes through the reactions associated with those gene ids are given in the other columns. The table shows the targets discovered and fluxes through the associated reactions are completely unchanged as δprogress is varied over a ranged of four orders of magnitude.(DOCX)Click here for additional data file.Table S5Boundary analysis. This table shows a subsection of a boundary analysis we performed on the set of reactions catalyzed by enzymes which are either experimentally proven or likely targets to achieve production of myrstiol-CoA (C14:0). Boundary analysis was performed by minimizing and maximizing each flux, while restricting the value of the biomass or production flux to a percentage of their maximum value. Column A indicates the catalyzing enzyme while column B shows the catalyzed reaction, identified the reaction codes used in the iAF1260 model. The lower and upper bounds for each reaction, while maintaining 100% biomass production, are shown in columns C and D respectively. While columns E and F show the lower and upper bounds respectively for each reaction while maintaining 100% production of myristiol-CoA. Green highlighted rows indicate reactions that must be increased in order to achieve 100% production of myristoyl-CoA when compared to 100% biomass production, while orange highlighted rows indicate those that must decrease to do so. Un-highlighted rows have overlapping flux boundaries while maintaining optimal biomass or production flux. Additional boundary analysis was carried out for varying percentages of maximum biomass and myristoyl-CoA production shown in “supporting information (DOCX)Click here for additional data file.Table S6Myristoyl-CoA production with set boundary limits. This table shows the production of myristoyl-CoA achieved by constraining all reactions associated with the set of enzymes listed in the first column within the boundaries found by boundary analysis. The percent constraint indicates the percentage of maximum production to which the network was constrained when doing the boundary analysis. For example 100% constraintis what was used in finding the boundaries shown in table S5 column E and F, since those boundaries were found while maintain 100% of maximum production flux. The production values are found by imposing the indicated combinations of boundaries on the iAF1260 model then optimized for minimization of the production of myristoyl-CoA (as done in the OptForce approach). All shown boundary combinations were tested in conjunction with a fadE knockout, without which no production was discovered.(DOCX)Click here for additional data file.Table S7Experimentally proven overproduction targets from Redirector. Redirector targets (target column) found for overproduction of different products (product column) are shown along with the base strain alterations needed to achieve the production experimentally and percent of the original production achieved. If no wild type strain is shown wild type production levels were too low to be a useful comparison (less than one percent of base line being used). Production levels are given as a percent of the original production of the strain being metabolically altered. Percentages were calculated by look at the ratio of total mg/L produced.(DOCX)Click here for additional data file.Table S8Redirector example design update and production. Uptake and export reactions fluxes comparing the flux distribution , production flux distribution  and the design used for (DOCX)Click here for additional data file.Table S9Boundary analysis of known fatty acid production targets for various production levels. Minimum and maximum possible flux values are shown for reactions catalyzed by known fatty acid production targets. Varying minimum and maximum values of reaction fluxes are given depending on required production level of either Biomass or C14:0-CoA. These requirements are implemented as lower boundaries placed on biomass and C14:0-CoA production, shown as a percent of their respective maximum possible flux values. The production required and the corresponding percentage are given for each column along with the term lower or upper, indicating the lower boundary or upper boundary on the possible flux space for the reaction in question.(XLS)Click here for additional data file.Text S1Supplementary methods. The text in this section provides additional information on the construction of the Redirector framework. First is a description of the construction of the redirection function. Second, the construction and usage of inclusion and exclusion variables is explained. It is then shown how these two elements are brought together into a Bilevel MILP formulation. Several methods for constructing redirection coefficient libraries are presented along with the cases in which each would be useful. Next, the iterative local search process used in the framework is presented, showing the progressive search method and how it is used. Finally, a list of variables used in the Redirector framework, and their importance, is given followed by some directions on best practices in using the Redirector approach. Supplementary results. This section includes a graph and discussion of Redirector optimization search times. A contrast of Redirector and flux boundary methods for production of fatty acids is examined. Finally, there is discussion of experimental validation of some of our targets.(DOCX)Click here for additional data file.


The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen’s system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNA’s performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with circadian rhythms. The software iNA is freely available as executable binaries for Linux, MacOSX and Microsoft Windows, as well as the full source code under an open source license. Chemical kinetics is by its very nature stochastic. This stochasticity has several origins, chief among them being that spontaneous processes are responsible for the conformational changes which occur in unimolecular reactions while the process of bringing two molecules together to participate in a bimolecular reaction is Brownian motion Current software implementations offer a broad range of stochastic modeling methods. Available packages can be divided into particle based descriptions and population based descriptions. Particle based methods adopt a microscopic approach that describes the movement of each individual reactant (non-solvent) molecule in space and time by means of Brownian dynamics. Popular software packages include the Greens Function Reaction-Diffusion algorithm A further reduced population description can be achieved by specifying to the situation in which the concentrations of interacting molecules are approximately spatially homogeneous over the entire reaction volume. Reaction kinetics is governed by two timescales: (i) the diffusion timescale, i.e., the time it takes for two molecules to meet each other and (ii) the reaction timescale, i.e., the time it takes for two molecules to react when they are in close proximity to each other. Concentration homogeneity over the entire compartment in which reactions occur, ensues when the reaction timescale is much larger than the diffusion timescale The chemical master equation (CME) is a mathematically equivalent and hence complementary description to the SSA In this article we introduce the software package, intrinsic Noise Analyzer (iNA), which enables a complementary approach using van Kampen’s system size expansion (SSE) of the CME together with traditional approaches of deterministic and stochastic simulation of chemical kinetics. The present implementation features the approximate computation of a selected number of moments of the probability distribution function solution of the CME by use of the Linear Noise Approximation (LNA) as well as the effective mesoscopic rate equations (EMREs). The advantage of these methods is that they are not based on ad-hoc assumptions like moment-closure approximations but rather they are based on the SSE which is a systematic expansion of the CME in powers of the inverse volume of the compartment in which reactions occur. The LNA provides the lowest order approximation to the second moments of the probability distribution (the variance and covariance of fluctuations) while the EMREs provide the first-order correction to the concentrations predicted by the deterministic rate equations (REs). iNA is the first software package to bridge the gap between deterministic simulation of chemical kinetics using rate equations, stochastic simulation of kinetics by the SSA and systematic analytic approximations of the CME. The novel combination of these complementary approaches makes iNA a valuable tool for the study of intrinsic noise in biological systems that has not yet been available to researchers and non-expert users in standalone software. The article is organized as follows. First we describe iNA’s input specifications, the implemented methods and the features of the GUI. We then present the use of iNA to explore the dynamics of three models commonly encountered in biochemical kinetics: non-cooperative enzyme kinetics, cooperative enzyme kinetics and a gene network associated with circadian rhythms. Finally we discuss the design and implementation of the SBML parser and the methods, along with optimizations that increase the performance of the analysis. We complete the presentation by a derivation of the SSE-based methods at the heart of iNA.http://code.google.com/p/intrinsic-noise-analyzer, as well as the full source code under the open source GPL2 license. The SBML files used in this article are available under the same URL.The software is available as executable binaries for Linux , MacOSX  and Microsoft Windows  from R chemical reactions of the typeThe general formulation of biochemical kinetics considers a number N of distinct chemical species confined in a mesoscopic volume of size j is the reaction index running from 1 to R, Xi denotes chemical species i, jk is the reaction rate of the thj reaction and ijs and ijr are the stoichiometric coefficients. We associate with each reaction a propensity function thj reaction to occur in the time interval in is the number of molecules of the thi species. Note that our general formulation does not require all reactions to be necessarily elementary, i.e., unimolecular and bimolecular chemical reactions, but can also describe effective reactions. If the thj reaction is elementary then its reaction rate jk is a constant while if it is non-elementary the reaction rate is a function of the instantaneous concentrations, i.e., the elements of the vector where mol, molecule numbers and derived units) and concentration .This description of the biochemical reaction networks in terms of reactants, products, the associated stoichiometries and kinetic laws are part of the Systems Biology Markup Language (SBML) The validation of models considered suitable for stochastic analysis requires the software to make several restrictions on SBML model definitions. Currently, events and explicit time dependent rate parameters are not supported. Also, reactions defined by the SBML specific reversible attribute cannot be validated for stochastic models due to ambiguities in the associated “KineticLaw”. We refer users to the software package Copasi which allows for convenient conversion between SBML’s reversible and irreversible reaction definitions. For consistency, the definition of a species must conform all species to be defined non-constant and free of algebraic constraints. The implementation of iNA assumes that such constraints arise naturally from the stoichiometry of the reaction network. Furthermore it is required for all parameters to be evaluated before runtime of simulations. Therefore the software does not allow parameters to be defined by ODEs or assignment rules. The software package gives the appropriate error messages in cases where one of the above specifications is not met.t, Gillespie proved using the laws of probability thj reaction to occur at time Over the past two decades the SSA has enjoyed widespread popularity mainly because of the ease by which one can simulate stochastic reaction networks j and a reaction time i. Note that the net change of the molecule number of species i by reaction j is given by the stoichiometric matrix The SSA generates a stochastic trajectory of the kinetics by sampling a reaction index An equivalent formulation for the stochastic reaction network described by Eq. (1) is the CME which can be derived from combinatorial arguments Here we have introduced the step operator which are exactly the same as those used in deterministic models of biochemical kinetics. Note that The leading order term of the SSE is given by the LNA which has been the key tool in analytical studies of noise iX and jX.The off-diagonal elements are the covariances which determine Pearson’s correlation coefficients between the concentration fluctuations of species Methods section). The EMREs are given byConsidering higher terms of the expansion one can obtain corrections to the REs which stems from a coupling of the mean concentrations to the higher order moments of the concentration fluctuations. These corrections have been calculated for networks composed of elementary reactions by Grima Methods for the definition of the vector where The present software allows the computation of the SSE methods either in time dependent conditions or at steady state. The former is obtained by numerical integration of the set of coupled ordinary differential equations, Eqs. (4), (6) and (9). The latter uses the same set of equations with the time derivative set to zero and reduces them to a set of simultaneous algebraic equations which typically can be solved with less computational effort and higher numerical accuracy. For the first time, all of the the above methods are made available to a broad audience by the software package iNA.The software iNA aims at ease of use of analytical approximations that facilitate the exploration of stochastic effects in biochemical reaction networks. We have therefore focused on a minimal GUI composed of a model tree with table and plot views. Analyses tasks can be easily accessed through wizards which guide the user through configuration. The GUI is divided into a menu bar and a main window. After a model has been loaded using the menu bar it will be available in the list of “Open models” on the left hand side. The latter list is hierarchically organized as followsModel, where the basic components of the model can be accessed. These include compartments, species, parameters and reactions; see Analyses, where the results of the Linear Noise Approximation, EMRE or SSA analyses can be accessed; see Model section contains a basic SBML reader for viewing the parameters that define the biological model and making sure that the SBML file has been parsed correctly. The Analyses section can be filled with items selected from the option Analyses in the menu bar. Currently there are three wizards available.The Steady State Analysis (SSE) wizard which customizes the computation of LNA, RE and EMRE in steady state conditions,a Time Course Analysis (SSE) wizard which customizes the computation of the LNA, RE and EMRE in time-dependent conditions,a Stochastic Simulation Algorithm (SSA) wizard guiding the initialization of stochastic simulations.a All wizards allow the user to select a subset of species to be analyzed, see Steady State Analysis is the most basic analysis provided by the program. It yields mean concentrations and the covariance matrix according to the LNA. Note that to the LNA level of approximation, the mean concentrations are the same as those obtained from solving the REs. The roots of the REs are computed by iNA using the Newton-Raphson method with line search Plot option shown in Time Course Analysis presents a wizard which is as simple to use as conventional integrators for deterministic REs by which one specifies the final time of integration, and the maximum relative and absolute errors. Therefore it is clear that all results obtained by the SSE should be checked for consistency with numerical integration carried out using smaller error estimates. The time course consists of theoretical estimates according to the deterministic REs and the corresponding fluctuations around it which have been estimated by the LNA at any point in time. At the same time the estimation of the mean concentrations using EMREs is shown and can be compared to its deterministic counterpart. The results can be accessed by a table view presenting the numerical data of the analysis or by selected plot views showing the mean concentrations and fluctuations computed by the REs and LNA, the correlation coefficients obtained from the LNA as a function of time or a comparison between the concentration predictions of EMREs and the REs.The Stochastic Simulation wizard offers the choice between two different implementations of the SSA (see section Design and Implementation) and allows the user to adjust the number of independent realizations that are used to calculate the statistical averages. This enables direct comparison of the simulation results with those obtained from the analysis using the SSE methods. All outputs are exportable to text files.In order to validate the results, the We showcase the utility of the present software by analyzing three models of biochemical kinetics: the Michaelis-Menten reaction The Michaelis-Menten reaction is a well studied example of biochemical kinetics. Over the past decade, stochastic models of the reaction have received considerable attention by means of analytical and stochastic simulation methods S denotes the substrate species, E the free enzyme species, ES is the enzyme-substrate complex and P the product species. The k’s refer to the associated rate constants. In what follows, we consider the same reaction occurring in two compartments characterized by two different length scales: the cellular scale which is the scale of large organelles such as mitochrondria  to take place in a compartment of volume Steady State Analysis. The output generated is a table view which is shown in X is defined as Steady State Analysis of iNA are very close to those predicted by the REs. This suggests that the LNA predictions of CV are accurate.The SBML file F1 specifies an initial condition of about 1200 enzyme molecules in non-complex form, which corresponds to a total enzyme concentration of Stochastic Simulation wizard; the result is shown in s. We then exported the data to a file and averaged over the output for We verified the accuracy of the LNA predictions by obtaining 1000 independent realizations using the Steady State Analysis performed by iNA is summarized in Next we study the same reaction in a compartment of reduced volume We verify these predictions by stochastic simulation; the result is shown in Methods, we use EMREs to calculate the theoretical value for the critical volume at which the concentrations of substrate and product become equal. Above the critical volume, the product concentration is larger than that of the substrate and hence the REs are qualitatively correct. Below the critical volume, the substrate concentration is larger than that of the product and REs are then qualitatively incorrect. The critical volume is calculated to be Comparing Apart from Michaelis-Menten kinetics, it is often found that many enzymes exhibit positive cooperativity in substrate binding. Such behavior is a kinetic signature of enzymes with multiple interdependent binding sites. As a consequence, experimental ligand binding curves show a sigmoidal dependence on the abundance of specific substrates thi enzyme reaction. This condition ensures that the binding of a substrate molecule to the enzyme molecule with n sites already occupied by other substrate molecules occurs quicker than substrate binding to an enzyme molecule with n−1 sites occupied; hence the phenomenon of positive cooperativity. In order to account for flux conditions that are found naturally in living cells, we also include substrate input and product removal reactionsWe enforce the condition We have written two SBML model files, F3 and F4, that describe the chemical reactions with an initial total enzyme concentration of Steady State Analysis of iNA enables one to obtain a quick overview of the noise characteristics of the reaction network in steady state conditions. Comparing the prediction of the REs and EMREs, as summarized in table view is An enzyme concentration of Time Course Analysis carried out by iNA shows transient damped oscillations in the mean concentrations, see We now use iNA to calculate the transient correlations in the dynamics. Note that the presence of correlations is a distinct feature of the stochastic description. The correlation coefficient as defined by Eq. (8) can be computed by iNA using the LNA, as well as from stochastic simulations, see Many enzymes operate in small compartments. Hence for physiological concentrations, the enzyme copy numbers can be quite small. In the second SBML model file, F4, we have reduced the compartmental volume to Many genes are represented by only a single copy inside living cells. It is also a fact that many important regulatory molecules exist in low copy numbers. Hence the biochemical process of gene expression is inherently stochastic which also implies that there is a significant amount of noise in the protein levels.A remarkable property of gene expression is the emergence of cellular rhythms which are commonly attributed to a negative feedback loop in which clock proteins inhibit the expression of their own gene We consider the case where cell-cell coupling and cell-to-cell variability are negligible. Then a single SSA realization of the stochastic dynamics of a circadian clock circuit models single cell circadian rhythms of clock expression while the average over independent realizations models the ensemble rhythm at the population level.G, the transcribed mRNA, M and the cytosolic clock protein, cP. Note that we have also taken into account mRNA degradation with rate dmk as well as the consumption of protein with rate dpk in a different pathway involving S which is not explicitly considered here. The negative feedback loop arises from transport of the cytosolic clock protein into the nucleus (the nuclear protein is represented by NP) The genetic network under study is a variant of the core model for a circadian clock which has been considered by Gonze and Goldbeter in Ref. The constraint that the gene copy number is fixed to one implies that the RE model for this system depends on the compartment volume. Taking into account discreteness, e.g., calculating the EMRE corrections, generates a volume dependence on top of this pre-existing volume dependence. To clearly distinguish the volume corrections due to the EMRE, we follow fl and 0.2fl respectively. M and NP are anti-correlated due to the onset of the repression. The minima in the correlations at some point in time suggests that repression generally affects the fluctuations of all three species.Two SBML files F5 and F6 were created to describe the biochemical reactions in compartments of size 2Time Course Analysis provided by iNA, according to the SSA, EMREs and the REs. Note that the EMRE predictions no longer agree with those of the macroscopic REs. In fact, we find that on the cell population level, the influence of intrinsic noise reduces the damping of synchronous oscillations compared to the large copy number case considered in It is commonly believed that on average transient responses observed on the cell population level can be accurately described by deterministic REs k1 by a factor of 100, see SBML file F7 in To investigate this effect further, we increased the repression rate constant We conclude by noting that the fact that the RE model could not capture the population level dynamics suggests that the common practice of extracting rate constants by fitting population level data to RE model predictions . We make use of the library Ginac, by means of which we can compute derivatives analytically and obtain series expansions of the mathematical model representation instead of resorting to numerical approximations. The computations are heavily based on basic linear algebra, for which we resort to the C++ template library Eigen The computational layer offers two methods for the stochastic simulation: the direct method developed by Gillespie Methods). Hence the complexity of the SSE based methods grows at least quadratically with the number of species depending on the algorithm of integration employed. In contrast, the performance of the SSA is limited first by the number of reactions over the time course, which is proportional to the size of the propensity and second by the large number of realizations required to obtain accurate statistical averages. We have addressed the latter issue by supplying our stochastic simulators with easy-to-use OpenMP parallelism which is available on many platforms and can be accessed through the Stochastic Simulation wizard. The remaining bottlenecks concern the performance of expression evaluation which is at the heart of both analytical and stochastic simulation methods. In order to allow for efficient evaluation of the required expressions, we have set up a bytecode interpreter, a concept which is common to dynamic programming languages. Bytecode interpreters increase the execution performance by reducing the code complexity and allow for very efficient implementations while at the same time maintaining the portability of code across many platforms. The expressions computed by iNA are first compiled into a bytecode representation which is then reduced by fast peep-hole optimizations Generally the number of simultaneous equations that need to be solved by the software is given by N for the REs, The Chemical Master Equation and the System Size Expansion we have introduced the CME, Eq. (3). The latter is typically intractable for analytical solution. In fact, exact solutions exist only for a handful of cases. However, the dynamics can be investigated systematically by means of van Kampen’s SSE In the section by which one separates the instantaneous concentration into a deterministic part given by the solution which takes into account the change in probability along the deterministic trajectory of The core of the expansion now follows from the observation that the step operator can be written as the Taylor series where We now turn to the expansion of the propensity which is done in two steps. Note that from here on we use the convention that twice repeated Greek indices have to be summed over 1 to N. First we expand the propensities in powers of epsilon. The result isNote that j-th reaction. Combining Eq. (20) and (21) we findThe first term denoted by In this way we obtain an expansion whose coefficients are independent of where and hence by collecting terms of order n>0. The above expansions are computed automatically by iNA and do not require any further user input. Note however that in the situation where the user defined propensity cannot be expanded in the prescribed way the software simply assumes that For non-elementary reactions we consider the Michaelis-Menten example with reaction propensity The expansion obtained in this way can be written aswhere the individual terms in the expansion are obtained using (3) together with the expansions (19), (20) and (21) and grouping terms in descending powers of n = 0, e.g., Note that we adopt the convention to omit the index for We now proceed by constructing equations for the moments of the The result is the Linear Noise Approximation which yields a linear Fokker-Planck equation. Its solution is well known to be a multivariate Gaussian distribution t = 0. We can also deduce by inspection of Eq. (35) that in this case we have Note that in the case of the deterministic initial conditions we have Using the definition of the covariance matrix where the Jacobian and diffusion matrix are given by In this section we will use higher order corrections to derive a set of effective mesoscopic rate equations, the EMREs, that are expected to be closer to the true concentrations as predicted by the CME. We therefore utilize the system size expansion, Eq. (27) together with Eq. (31) and equate terms of the order Multiplying the above equation by We can use the above result together with Eq. (17) and (32) to find an equation for the average concentration accurate to order Note that in the case of deterministic initial conditions this result enjoys an increased accuracy of order Recently, Ramaswamy et al. We here derive the equation for the critical volume for this discreteness-induced concentration inversion of substrate and product in the Michaelis-Menten scheme (10). The macroscopic REs are given bywhere Using the rate constants for the Malate dehydrogenase enzyme summarized in


The genus Cyanothece includes unicellular nitrogen-fixing cyanobacteria that have been shown to offer high levels of hydrogen production and nitrogen fixation. The reconstruction of quality genome-scale metabolic models for organisms with limited annotation resources remains a challenging task.Cyanobacteria are photoautotrophic prokaryotes that exhibit robust growth under diverse environmental conditions with minimal nutritional requirements. They can use solar energy to convert COCyanothece strains, namely Cyanothece sp. PCC 7424, 7425, 7822, 8801 and 8802, as the genome-scale metabolic reconstructions iCyc792, iCyn731, iCyj826, iCyp752, and iCyh755 respectively. We compare these phylogenetically related Cyanothece strains to assess their bio-production potential. A systematic workflow is introduced for integrating and prioritizing annotation information from the Universal Protein Resource (Uniprot), NCBI Protein Clusters, and the Rapid Annotations using Subsystems Technology (RAST) method. The genome-scale metabolic models include fully traced photosynthesis reactions and respiratory chains, as well as balanced reactions and GPR associations. Metabolic differences between the organisms are highlighted such as the non-fermentative pathway for alcohol production found in only Cyanothece 7424, 8801, and 8802.Here we reconstruct and subsequently analyze and compare the metabolism of five Our development workflow provides a path for constructing models using information from curated models of related organisms and reviewed gene annotations. This effort lays the foundation for the expedient construction of curated metabolic models for organisms that, while not being the target of comprehensive research, have a sequenced genome and are related to an organism with a curated metabolic model. Organism-specific models, such as the five presented in this paper, can be used to identify optimal genetic manipulations for targeted metabolite overproduction as well as to investigate the biology of diverse organisms. Cyanothece ATCC 51142, iCyt773, was recently published [iCyt773 is an improvement upon the previously published iCce806 model [iCce806 [iCyt773 also models the diurnal rhythm of the Cyanothece metabolism. Since Cyanothece ATCC 51142 is closely related to all five Cyanothece species discussed in this paper [Cyanothece PCC 7424, 7425, 7822, 8801, and 8802, as iCyc792, iCyn731, iCyj826, iCyp752, and iCyh755 respectively  are the collection of gene to protein to reaction associations (GPRs), charge and elementally balanced reactions, and constraints on molecular functions found within a cell -4. The cublished . It cont[iCce806 . Further[iCce806 . iCyt773is paper , it was Cyanothece belongs to the phylum of Cyanobacteria. Cyanobacteria have a number of properties that make them ideal candidates for bio-production. Photosynthetic cyanobacteria bypass the need for sugar carbon substrates while having higher solar energy conversion efficiencies  than C3 (2.4%) and C4 plants (3.7%) [Cyanothece generate not only hydrogen [Cyanothece possess the potential to grow in air and can be easily fixed to solid matrices [Cyanothece PCC 7425 is the only species that is not capable of accomplishing this task in an aerobic environment [The genus s (3.7%) . Cyanothhydrogen ,14-16 buhydrogen ,18. In amatrices . All fivironment . 7425 alironment .Cyanothece PCC 7424, 7425, 7822, 8801, and 8802, were all sequenced following the promising discoveries made concerning the metabolic capabilities of Cyanothece ATCC 51142 [Cyanothece genomes [CC 51142 . These f genomes . Metabol genomes  have bee genomes , it is iEscherichia coli K-12, the strain modeled in the iAF1260 metabolic reconstruction [Cyanothece PCC 7424 (271) [There exist numerous databases devoted to gene annotations for a wide variety of organisms -27. Howetruction , has app24 (271) -31. This24 (271)  may alsoCyanothece species using iCyt773 and reviewed annotations from Uniprot [iCyt773 model and the SEED database [iCyt773 and SEED reactions or metabolites was required as iCyt773 was initially constructed using SEED notation when possible. The five models are all capable of producing biomass using the iCyt773 biomass equations under diverse nutrient conditions. All five models are free of thermodynamically infeasible cycles, and the fractions of reactions mapped to specific genes  are within the range of manually curated reconstructions. The use of multiple annotation sources helps to mitigate errors that may arise from a single source. Unlike automated draft models , organiyanothece, but areiCyt773, with reactions taken from the SEED database whose presence in that organism were confirmed by reviewed annotations. The statistics for the five developed models are shown in Table Cyanothece 8801 and 8802 have no unique reactions though they do contain a set of 30 reactions that are not found in any other reconstruction. All five models contain four compartments: cytosol, periplasm, thylakoid lumen, and carboxysome. The number of genes present in each reconstruction is similar to the number of open reading frames (ORFs) associated with the iCyt773 and iSyn731 models. The percentage of non-exchange reactions without associated genes falls within ranges comparable to those of numerous manually curated models  oxidoreductase present within iCyn731. The other four models contain another Fe(II) oxidoreductase. The number of reactions shared between each of the five models and iCyt773  [nifK in the fixation of nitrogen. In iCyj826 this gene is involved in the GPR of the nitrogen fixation reaction present within the model. Given that the GPR describes nifK as one of three critical subunits of the enzyme, its deletion results in the inability for that reaction to carry flux. Upon its removal from iCyj826, the model is unable to grow without the addition of nitrate or ammonium, showing that the model reacts to the knockout in the same manner as the organism does in vivo.The effect of a gene knockout on an organism’s phenotype is frequently used in assessing GSM quality ,38. HowePCC 6803 ,40, noneCyanothece 7424 and 7822 as reflected in the models. 2-oxoglutarate decarboxylase and succinic semialdehyde dehydrogenase, found in many cyanobacteria, complete the TCA cycle despite the absence of 2-oxoglutarate dehydrogenase [iCyt773, and were transferred to all five models. The associated genes are also bidirectional best hits with the two genes in Synechococcus PCC 7002 that are associated with the aforementioned enzymes [iCyn731, iCyp752, and iCyh755 all contain an alkane biosynthetic pathway similar to what is present within iCyt773. While iCyt773 contains the pathway that enables the production of pentadecane from hexadecenoyl-ACP, Schirmer et al. have measured heptadecane but not pentadecane production from Cyanothece 7425 [iCyn731 contains only heptadecane production, while iCyp752 and iCyh755 contain pathways for both pentadecane and heptadecane (no specific literature evidence neither in support nor in conflict with this was found). The two enzymes required, hexadecenoyl-ACP reductase and hexadecenal decarbonylase (enzyme commision (EC) numbers 1.2.1.80 and 4.1.99.5 respectively per iCyt773), have no corresponding annotations or orthologous genes in Cyanothece 7424 or 7822 [Despite the many similarities between the five species, significant differences also exist . Genes trogenase . Both of enzymes . iCyn731Cyanothece 7424, 7425, and 7822 all contain the enzymes keto-thiolase and acetoacetyl-CoA reductase, which are necessary for the synthesis of polyhydroxyalkanoic acids [E. coli[kivD gene from Lactococcus lactis[adh2 gene from Saccharomyces cerevisiae[kivD gene codes for a 2-keto acid decarboxylase that acts on a wide range of substrates and enables the conversion of the 2-keto acids into aldehydes. The workflow identified genes in Cyanothece 7424, 8801, and 8802 which are bidirectional best hits with the kivD gene from Lactococcus lactis, and also annotated as being associated with the same EC number as kivD. An alcohol dehydrogenase, such as adh2, then converts these aldehydes into alcohols. The adhA gene (slr1192) in Synechocystis PCC 6803 has been found to have wide substrate specificity that includes the aldehydes associated with butanol and propanol [Cyanothece 7425 had e-values on the order of 10-28 and percent identities of 30%, the searches, both forward and reverse, for the other four organisms had e-values ranging between 10-138 and 10-153 with percent identities ranging from 58 to 61%. The presence of orthologs to both a 2-keto acid decarboxylase and alcohol dehydrogenase with wide ranges of specificity in Cyanothece 7424, 8801, and 8802 provides annotation evidence for the hypothesized presence of non-fermentative higher alcohol pathways [Polyhydroxyalkanoates (PHAs) are a complex family of polyesters that can be synthesized by a wide variety of bacteria . Cyanothic acids -45. Theric acids . The sam [E. coli,47 afterus lactis and the erevisiae. The paterevisiae. The kivpropanol . All fivpathways .Cyanothece 51142 does not contain the associated genes for the conversion of agmatine to putrescine, and this is reflected in the iCyt773 model [iCyc792 and iCyj826 contain agmatinase and urease. The proposed pathway for agmatine breakdown into putrescine in Cyanothece 7425, 8801, and 8802 is through N-carbamoylputrescine. The two reactions required for this degradation can be found in all three associated models. Finally, as predicted by Bandyopadhyay et al. [iCyc792, iCyj826, iCyp752, and iCyh755 contain the reactions required to break putrescine down into spermidine and spermine.Significant variations in nitrogen metabolism between the five species has been documented . Arginin73 model ,12 as thiCyt773. The diverging nitrogen metabolism reactions were retrieved using SEED, as agmatine is the preferred polyamine for Cyanothece 51142 [Clostridium species [Cyanothece 7425 is the only organism to contain the complete pathway. The alcohol dehydrogenase exists within the models given the identification of homologs to the Synechocystis adhA gene [Clostridium acetobutylicum ATCC 824. Given the lower e-value for Butanoyl-CoA dehydrogenase, it is the gene most likely to not be present or functional within Cyanothece 7425. The enzymes present in the five pathways mirror the phylogenetic relationship trends of the five species in a manner comparable to what was initially seen in the reaction similarities from Figure Additional reactions retrieved using reviewed annotations have provided a number of insights into the five species that would not have been either found or confirmed if reactions were only pulled from ce 51142 . An altece 51142 . The coe species ,54. FigudhA gene . The 742iCyt773. All five models are capable of converting galactose-1-phosphate to fructose-6-phosphate as in iCyt773. Three of the models, iCyn731, iCyj826, and iCyh755, also include the reaction that converts galactose into galactose-1-phosphate, enabling them to process galactose in the glycolysis pathway. Tetrahydrobiopterin (BH4) is a pteridine compound that acts as a cofactor for nitric oxide synthases and aromatic amino acid hydrolases in higher animals [Synechococcus PCC 7942 acted on BH4 [iCyt773 does not contain the complete BH4 pathway as described by Thony et al. [Synechococcus PCC 7942. The reaction was not included in the models, as it does not exist within the SEED reaction database. All enzymes that were retrieved from annotations but were not included in the model because of a lack of associated reaction in the subset of the SEED database used for model development are listed in Additional file The proposed workflow also served to complete unfinished pathways from  animals , and thed on BH4 . Even thiCyt773 offer insight into divergences between the metabolism of the new organism and the reference model. Two of the reactions that were not transferred from iCyt773 to the models for Cyanothece 7424 and 7822 are responsible for the conversion of hexa- or octadecenoyl-ACP to n-hepta or pentadecane. As previously mentioned it is accepted that the alkane biosynthetic pathway does not exist in these organisms [iCyt773 can produce xanthine from either hypoxanthine or xanthosine, iCyc792 only contains the reactions for production from xanthosine and cannot break xanthine down into uric acid. iCyn731 only contains the reactions for production from hypoxanthine, but can convert xanthine into uric acid. The other three species do not contain any reactions involving xanthine and thus cannot process purine ribonucleotides through this pathway. Six reactions involved in transporting metabolites between the cytoplasm and periplasm or extracellular space were not transferred, such as molybdate transport via the ABC system. Given the likelihood that such reactions still exist within the other Cyanothece strains, it is possible that the associated GPR in iCyt773 should be reevaluated for these reactions.Reactions not transferred from Current model development methods can be generally characterized as manual, semi-automated, or automated. The workflow presented in this paper is best classified as semi-automated. This workflow allows for more expedited model development while avoiding some of the sources of error plaguing automated model generation and allowing for a wide range of customization. This workflow can be adapted for use with any models, annotation sources, and additional reaction sets given annotation availability and user preferences.-5. Here we use a more conservative cutoff of 10-30 to safeguard against such instances. When the cutoff was relaxed from 10-30 to 10-5 for the bidirectional BLAST between Cyanothece 51142 and the five species there were between 280 and 403 additional best hit pairs for each of the organisms. The number of these pairs that involved genes present in iCyt773 varied between 15 for Cyanothece 7424 and 8801, and 26 for Cyanothece 7425. The reliance of manually constructed models on reviewing every annotation and manually curating the model greatly increases the time spent on development. This workflow helps to mitigate the need for manual review of each annotation by only using annotations that are reviewed or are derived from reviewed sources. Manual curation can then be reserved for certain key steps. Some of these models only include additional reactions beyond those retrieved from the curated models if the reactions are required for biomass production [Many draft models are nowadays generated through the identification and comparison of homologs with the GPRs of curated models -61. Hamioduction ,60,61. TCyanothece models created using the MIRAGE method contain generalized lipids along with a non-specific acceptor metabolite [Cyanothece 7424 contain menaquinone and ubiquinone, compounds shown to not exist within that organism [There are a number of approaches for the automated development of metabolic reconstructions ,62-64 aforganism . Conversorganism ,62,64. APenicillium chrysogenum model iAL1006 [Other methods that combine manual and automated steps provide their own distinct approach to model reconstruction. The RAVEN toolbox  allows f iAL1006 . Our worCyanothece strains using the previously published iCyt773 model and reviewed annotations from numerous sources. The comparisons between these five models line up with the established phylogenetic relationships between the species. Specific reactions that were both kept from being taken from iCyt773 or added from the SEED database demonstrate the efficacy of this workflow and provide insights into the metabolism of the five species, as well as suggesting areas for further curation in the iCyt773 model. This workflow can easily be adapted to work with other metabolic models, annotation sources, and reaction databases. All five models  are included in the supplementary material.In this paper we presented a workflow that was used to rapidly develop curated models for five Cyanothece 51142. Reactions that were determined to exist in both Cyanothece 51142 and the organism being modeled were transferred from iCyt773 to the draft model. This reaction sharing was established through a comparison of homologs between the two genomes. These homologs were determined using a bidirectional BLAST search between the genomes of Cyanothece 51142 and the organism, using an e-value cut off of 10-30 and the requirement of mutual best hits. The Boolean logic given by each GPR in iCyt773 was evaluated using these bidirectional hits. If the organism contained the homologs required to satisfy the logic and encode the protein, the reaction was transferred to the draft model. This only requires one isozyme to be present within the organism , yet requires that all genes that code for an essential protein complex have a homolog. These identified reactions were added to the draft model with the GPRs modified to reflect the homologs present in the organism. Both the homology searches and identification of reactions to be included in the model were automated steps.Draft models for the five organisms were developed using the workflow shown in Figure Cyanothece 7424 gene PCC7424_1895. Both Uniprot and NCBI Clusters assigned the EC 2.5.1.75 to the gene, whereas the RAST method assigned the EC number 2.5.1.8. Despite the apparent mismatch, EC 2.5.1.8 had previously been transferred to 2.5.1.75, resolving any conflict between the annotations. If the enzymes are uniquely classified, a search of literature, specifically the InterPro database [Cyanothece 7424 gene PCC7424_2477 has an associated annotation of 1.1.1.29 from iCyt773, whereas RAST assigns both 1.1.1.26 and 1.1.1.81 to the gene. InterPro states that the 1.1.1.26 enzyme belongs to a protein family that is found in hyperthermophilic archaea, thus ruling out its existence in Cyanothece 7424. After using the InterPro information to rule out a possible associated enzyme, the annotation is resolved through order of confidence (described below), and 1.1.1.29 is attributed to the gene. Next, any enzymes that are associated with generic metabolites, or metabolites known to not be found within the organism, are removed. Such filtering can be seen with the Cyanothece 7425 gene Cyan7425_1569. Both the model and RAST annotation suggest that succinate dehydrogenase (1.3.99.1) is associated with this gene. However NCBI Protein Clusters suggests enzyme 1.3.5.1, which is a succinate dehydrogenase specific to ubiquinone. As ubiquinone is not present within Cyanothece[iCyt773, Uniprot, NCBI, and RAST. The order of confidence is derived from the likelihood that a source has been manually reviewed and is applicable to the individual gene in question. iCyt773 GPR relationships were curated specifically for a Cyanothece model. Uniprot reviewed annotations are manually annotated individually [iCyt773, the annotation is not listed as conflicting and the enzymes from the model are used. There were on average between 40 and 50 genes with conflicting annotations. Between 55 and 70% of conflicts required order of confidence to resolve. Using multiple sources allows for the identification of probable errors in the databases. These annotations can also reveal errors in other databases not used in the model development. One such example is gene PCC7424_2817 in the Cyanothece 7424 genome. All sources used in this paper, along with KEGG Orthology [Reviewed annotations retrieved from Uniprot , NCBI Prdatabase , is thenyanothece, this covidually , and RASvidually ,67. Lowerthology , indicatrthology  annotatiiCyt773 model. Reactions with a matching EC number are retained, and the remaining EC numbers are used to retrieve reactions from the SEED database [iCyt773 are removed while the remaining reactions necessary for photosynthesis are included. These reactions are known to exist within the organisms, as they can grow autotrophically. Any oxidative phosphorylation reactions or diffusion transport reactions that had not previously been added to the model are appended given their obvious essentiality. This set of reactions constitutes the draft model. All steps in draft model development are automated except for the EC annotation reconciliation. The time required to complete this step is reduced as more models are developed, and results can be applied to related organisms.Subsequently, this resolved list of EC numbers is referenced against the database . Reactiodatabase , as thesiCyt773 model were used in the five models [iCyt773 that did not have direct literature or annotation evidence were included in order to produce biomass. A substantial number of these reactions did not have both a gene and enzyme associated in iCyt773, which would lower their chance to be included during the initial stages of draft model development  were removed. Additional file The models were further modified to avoid the presence of thermodynamically infeasible cycles. Flux variability analysis was performed to identify unbounded reaction fluxes. Given the absence of thermodynamically infeasible cycles within iCyt773 reactions or the analysis of retrieved annotations. Bidirectional best hits were previously used to evaluate the presence of each reaction in the new organism. If a reaction is added to the model, the GPR for every isozyme or complete subunit that is present is translated to the list of genes for the new organism.GPR relationships were primarily derived from either the previous bidirectional BLAST analysis of iCyt773 because of either proof of their existence (e.g. photosynthetic reactions) or their requirement for biomass production. Many of these GPR relationships are missing a small number of bidirectional best hits. For these genes the BLAST cutoff was reduced to 10-10. These few additional best hits aided in the resolution of many of the remaining reactions, leaving between six and thirteen of the reactions without a transferred GPR.The GPR relationships for reactions retrieved from SEED were developed by applying the Autograph method . All genFlux balance analysis  was usedMaximize vBiomassSubject toij is the stoichiometric coefficient for metabolite i in reaction j, vj,min and vj,max denote the minimum and maximum flux values for reaction j, while vj represents the flux value of reaction j. N and M denote the total number of metabolites and reactions respectively.Where SA mixed integer linear program was used in the determination of a minimal set of reactions necessary for biomass production using the following formulation.Subject toj, which when equal to zero eliminates flux through reaction j. The value of y for all reactions present in the draft model was fixed at one. Biomass production was fixed at greater than 1% of the maximum value when all iCyt773 reactions were included, and the number of included reactions was minimized.All reactions were assigned a binary variable yFlux variability analysis was used for identification of reactions present within cycles, and used the following formulation.No constraints were placed on the biomass growth so as to identify all possible cycles within the model. This analysis was performed iteratively after each series of modifications was made to the reactions present within the cycles.The reaction similarity between any two models is calculated using the following formula,A denotes the total number of shared reactions between the two organisms, whereas B and C represent the number of unique reactions in each model.CPLEX solver (version 12.3 IBM ILOG) was used in the GAMS  environment for solving the optimization models. All computations were carried out on Intel Xeon X5675 Six-Core 3.06 GHz processors that are a part of the lionxf cluster, which was built and operated by the Research Computing and Cyberinfrastructure Group of The Pennsylvania State University. All codes used in model development were written using the Python programming language.The authors declare that they have no competing interests.TJM designed model development workflow and developed models; TJM, BMB, HBP, and CDM analyzed the data; TJM and CDM wrote the paper. All authors read and approved the final manuscript.All five genome-scale reconstructions , along with GPR and metabolite information.Click here for fileA zipped file containing all five genome-scale reconstructions , along with GPR and metabolite information in SBML format.Click here for fileList of retrieved EC numbers which were not associated with any reactions in the SEED subset of reactions used for draft model development.Click here for fileList of reactions removed from the five models for containing generic metabolites.Click here for fileSet of reactions added to each model to insure biomass production, along with associated support for inclusion.Click here for fileAll reaction modifications made to eliminate thermodynamically infeasible cycles.Click here for file