A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined  Obesity is becoming a growing health problem, with the risk of running into a disease state called the Metabolic Syndrome (MetS). It is difficult to study MetS in humans as it develops over a long period of time while many processes and organs are involved. Moreover, each patient may present itself with different characteristics. We combined data from animal experiments with a computer model and computer simulations to study the development of MetS. The new model correctly predicts which changes in the underlying metabolic processes could explain the MetS symptoms. Unexpectedly, two different subgroups were identified: those with high cholesterol and high triglycerides, and those without. The computer model found that in those who develop lipid abnormalities, both dietary cholesterol absorption and hepatic liver fluxes were higher. The simultaneous presentation of obesity, dyslipidemia, insulin resistance and hypertension is generally referred to as the Metabolic Syndrome (MetS) –5. Togetet al. [et al. [Modeling efforts in the past have shown that systems biology can be a powerful approach to gain both qualitative and quantitative insight in the inherently complex systems that drive the development of MetS. For example, Lu et al.  demonstr [et al.  have ideHowever, these computational models were designed to model the healthy ,20–29 orIn addition, a long-term simulation method has been developed referred to as Analysis of Dynamic Adaptations in Parameter Trajectories (ADAPT) –38. It iin silico MetS model that describes the metabolic processes involved in whole-body carbohydrate and lipid metabolism, and integrated with iii) time-series data obtained from an in vivo MetS model. The APOE*3-Leiden(E3L).CETP mouse [Therefore, we aimed to design a computational, data-driven approach to study the longitudinal and progressive dynamics of the majority of metabolic alterations of MetS, i.e. obesity, glucose intolerance, insulin resistance and dyslipidemia. We employed a systems biology methodology that integrates three main concepts to infer metabolic adaptations during MetS development: i) the long-term simulation method ADAPT, combined with ii) a newly developed TP mouse ,42 is a TP mouse ,43–51. WTP mouse ,52 by coin silico modeling quantitatively analyzes and integrates the experimental data and provides estimates of metabolite concentrations and fluxes that were experimentally not measured. With this modeling approach, we demonstrate when and how the onset and development of MetS occurs. Although we expected to find a homogeneous population, our modeling approach shows the emergence of different phenotypes of MetS. This heterogeneity is associated with differences in intestinal and hepatic metabolic fluxes.Our in vivo data of the onset and progressive development of MetS have been collected from 11-week-old male E3L.CETP mice that were fed diets differing in fat and cholesterol content and were followed for three months. These diets comprised of a low-fat diet , high-fat diet  and a high-fat diet with additional dietary cholesterol . For each diet group, longitudinal data was obtained throughout the time course of the study: body weight was monitored weekly, plasma markers were measured monthly and liver lipids were assessed after three months. We combined data-driven and physiology-based modeling. Hereto we integrated prior knowledge on the complex metabolic systems that underlie the pathophysiology of MetS with experimental observations on the actual metabolic status over time: As compared to the HFD alone, obesity development was slightly increased by cholesterol feeding , as moniAs compared to HFD, plasma triglyceride (TG) levels were significantly increased after three months of feeding HFD with cholesterol . CholestDLP; n = 3) and the other mode as the non-dyslipidemic Metabolic Syndrome phenotypes . This subdivision shows a consistent pattern in both TG and TC at the three months’ time point, but is already present earlier in time. In fact, the onset of dyslipidemia is already noticeable after two months of the diet, and progresses further towards the three months’ time period. Note that the subdivision in phenotype development is a result of the HFD+C diet; no baseline differences are observed (t = 0 months in this data set), and these observations are limited to the HFD+C group and not present in HFD.Male E3L.CETP mice developed HFD-induced obesity, glucose intolerance and dyslipidemia, mimicking the classical symptoms seen in human MetS. However, the high variability in both triglyceride and cholesterol levels complicated the interpretation of the dyslipidemic component. Therefore, we also presented the data of mice fed with the HFD+C individually in the right-hand side panels of DLP individuals are significantly more insulin resistant than the MetSnon-DLP individuals after at the three months’ time point. This trend is even more profound in the insulin dynamics in response to a glucose challenge test  is composed of a system of coupled, nonlinear ordinary differential equations (ODEs). The steady state of the ODE model represents a snapshot of the metabolic state and describes the mass balance of the metabolite pools and flux rates for carbohydrate, lipid and cholesterol species in the plasma, liver, intestinal lumen and periphery .Next, we developed a novel eriphery . The modin vivo data whilst considering four subgroups: the LFD group, HFD group, MetSnon-DLP phenotypes and MetSDLP phenotypes. For each subgroup, MINGLeD was fitted to the data of each of the four time snapshots separately. The resulting sixteen models differ in the values for their estimated parameters. For each model the parameter estimation procedure was repeated with 500 different initial parameter sets using multi-start optimization. MINGLeD was integrated with the non-DLP and MetSDLP). However, this ignores the fact that the phenotypes represented by those four models are causally connected in time. MINGLeD describes metabolic fluxes and concentrations but does not explicitly include the multiple pathways that regulate and modulate metabolism over a three-month time period (such as changes in gene expression and protein activity). Both limitations were overcome by combining MINGLeD with a dedicated approach for longitudinal modeling of biological systems: ‘Analysis of Dynamic Adaptations of Parameter Trajectories’ (ADAPT) [in vivo data, sampled datasets are generated and for each sampled dataset a parameter trajectory was estimated. This was repeated resulting in a set of 1,000 simulated models yielding a database comprising of in silico populations of 1,000 virtual individuals for each subgroup. Each simulation describes the experimental data adequately, though with variation in parameter trajectories yielding differences in fluxes and concentrations, especially for model variables that are not experimentally observed. A more detailed explanation of the ADAPT methodology is given in the Online Methods.Calibration of MINGLeD yielded separate models for each subgroup  –38. ADAPin vivo data points accurately and provide a continuous description of the dynamics with which the system behaves over time, illustrating the different trajectories for the different subgroups. Note that ADAPT did not yield one single simulation but provided ensembles of state and flux trajectories. Each line in in silico model accurately captures the trends as observed in the in vivo data. The ensembles of simulated concentration and flux trajectories provide insight in how the underlying metabolic network is affected upon emergence of the two different MetS phenotypes. We showed that the Despite equal intake of food and thus cholesterol, dietary cholesterol absorption from the intestinal lumen was markedly higher in the dyslipidemic compared to the non-dyslipidemic MetS group , which mThe modeling also predicted that within the dyslipidemic phenotype, rates of lipid shuttling towards (V)LDL-TG uptake  were incnon-DLP) and HFD+C (MetSDLP) groups  groups .DLP phenotype. This aspect could also be observed in the gene expression data: the expression of bile acid synthesis genes nuclear farnesoid X receptor (FXR) and Cholesterol 7 alpha-hydroxylase (Cyp7a1) was largely upregulated, as compared to HFD alone.de novo lipogenesis (FASN), Acetyl-CoA carboxylase 2 (ACC2), acyl-CoA:diacylglycerol acyltransferase 2 (DGAT2) and sterol regulatory element binding protein 1c (SREBP1c) were all largely downregulated probably as a compensatory mechanism.Hepatic ogenesis ; DNL is PPARα), Peroxisomal acyl-coenzyme A oxidase 1 (ACOX1) and Carnitine palmitoyltransferase 1a (CPT1a). Collectively, these predictions suggest more lipid accumulation in the liver of the dyslipidemic mice.In addition, the hepatic β-oxidation  is predisilico predictions at the last time point. Indeed, addition of cholesterol did lead to an increase in lipid turnover and the hepatic lipid pool sizes as compared to the high-fat diet without cholesterol, both in the dyslipidemic and non-dyslipidemic phenotype  and reduced insulin sensitivity (pre-diabetes). This demonstrates that our modeling approach can be used to study the onset and progression of MetS as well as its co-morbidities. From the heterogeneous dataset our model identified differences among tested individual mice. Unexpectedly, the existence of two different phenotypes in MetS development was predicted.in vivo model did show heterogeneity in phenotypic presentation. In addition, the manifestation of the full repertoire of metabolic alterations associated with MetS makes this a useful in vivo model, whereas other animal models only describe one or partial metabolic aspects of MetS [The clinical presentation of MetS in humans is highly heterogeneous and spans over decades. Male E3L.CETP mice fed a high-fat diet supplemented with cholesterol develop MetS within a time scale of several months. Although all of these animals have the same genetic background, received the same diet and were kept and monitored in a controlled, standardized environment, this  of MetS –59.Using a traditional statistical approach, both this heterogeneity and limited datasets comprising of low number of animals are problematic. Moreover, the time-dependency of the data–i.e. individual data of consecutive points in time are interrelated and therefore not independent samples–would further complicate analysis. Our computational modeling approach tackles these problems by combining MINGLeD with ADAPT. Contrary to other computational models, MINGLeD integrates both glucose and lipid species at a whole-body level. Both carbohydrates and fats are of importance in MetS and MINGLeD allows for simultaneous description of these key components in terms of both metabolite pool sizes (concentrations) and metabolic fluxes. Complexity and detail in model equations was considered in close relation to what is experimentally feasible to measure throughout long-term MetS development. Therefore, MINGLeD’s data-driven, physiological design allows for describing both flux and concentration data on a whole-body level. MINGLeD per se can be simulated to describe metabolic snapshots, whereas the long-term dynamics are captured by using MINGLeD in conjunction with ADAPT. ADAPT has been designed to work with this kind of data and makes use of the time-dependent observations and simultaneously assesses uncertainty based on the variability in the data. The strength of the ADAPT methodology in dealing with heterogeneity became evident with the identification of two distinctly different phenotypes despite the limited number of animals that were studied. These two phenotypes mainly differ in terms of dyslipidemia, and flux trajectory analysis pinpointed differences in: 1) hepatic turnover of metabolites, including lipid fluxes and 2) the intestinal cholesterol absorption. This appears to mimic the observation in humans showing that levels of cholesterol absorption efficiency can vary greatly among individuals ,61. Thesin vivo and in silico information allows to combine pre-existing knowledge with experimental quantitative data and can therefore be applied to study other multifactorial, progressive diseases where longitudinal data are available. A future application of the model is to quantify energy intake and energy expenditure and analyze the energy balance over time for development of obesity and MetS.The methodology of integrating In conclusion, we combined data from animal experiments with a computer model and computer simulations to study the development of MetS. The new model predicted which changes in the underlying metabolic processes could explain the MetS symptoms. Two different subgroups were identified: those with high cholesterol and high triglycerides, and those without. The computer model found that in those who develop lipid abnormalities, both dietary cholesterol absorption and hepatic liver fluxes were higher.2 inhalation.All animal experiments were performed in accordance with the regulations of Dutch law on animal welfare, and the Animal Ethics Committee of the Leiden University Medical Center, Leiden, The Netherlands. Animals were sacrificed by COin vivo data at different stages during the development of the Metabolic Syndrome. To this end we use male APOE*3-Leiden(E3L).CETP transgenic mice as diet-induced in vivo model to study the metabolic adaptations that occur over time.The first step of our systems approach involves the gathering of Male E3L.CETP transgenic mice were housed under standard conditions with a 12 h light/dark cycle (7AM-7PM), housed with 1–2 animals per conventional cage with free access to chow diet and water, unless indicated otherwise. At the age of 11 weeks, randomized according to body weight and plasma lipids  and glucose, mice were divided into three groups: mice were fed either a low-fat diet , high-fat diet  or a HFD with additional cholesterol   for three months. The LFD has a 20% energy content derived from lard and contains 3.8 kcal/g diet; the HFDs have a 60% energy content derived from lard and contain 5.2 kcal/g diet . The specific composition of each diet is listed in de novo lipogenesis was determined by using an isotope tracer. For further details on the experimental setup the reader is referred to During the study, body weight and food intake were measured weekly, body composition (lean and fat mass) every other week. Blood samples were taken monthly and analyzed for glucose, insulin, free fatty acids, total cholesterol, HDL-cholesterol and triglycerides. At the end of the three months dietary induction experiment, animals were sacrificed. Livers were isolated for measuring lipid metabolites and gene expression, and the hepatic in silico model describing MetS onset and progression. To this end we have developed a novel dynamic, computational model called Model INtegrating Glucose and Lipid Dynamics (MINGLeD). This model is tailored to describe data from longitudinal studies and involves the metabolic system governing carbohydrate, lipid and cholesterol metabolism. It is composed of a system of coupled, nonlinear ordinary differential equations (ODEs). The steady state of the ODE model represents a snapshot of the metabolic state and describes the mass balance of the metabolite pools and flux rates for carbohydrate, lipid and cholesterol species in the plasma, liver, intestinal lumen and periphery. This in silico model aims to describe the metabolic system in a whole-body perspective under healthy conditions as well as at different stages during Metabolic Syndrome development.The second step of our systems approach involves the development of a dedicated The steady state of MINGLeD describes the average behavior of the metabolic system over the time course of one day. Therefore no specific postprandial or fasting periods have been included explicitly. The metabolic pathways that are important in describing the metabolic system are presented in de novo lipogenesis (DNL) and cholesterol biosynthesis. Bile acid synthesis, biliary bile acid and cholesterol excretion, enterohepatic reuptake, fecal excretion of bile acids and cholesterol. Finally, metabolism of acetyl coenzyme A in hepatic and peripheral tissues has been included.MINGLeD describes metabolite pools originating from carbohydrate substrates , lipid species  and cholesterol . The metabolic pathways that define the interactions between these metabolites include the uptake of dietary macronutrients, glycolysis, hepatic gluconeogenesis, lipoprotein assembly and (remnant) uptake, cholesteryl ester transfer between lipoproteins , trans-intestinal cholesterol excretion (TICE), exchange between free cholesterol and cholesteryl esters (via ACAT and CEH) in hepatic tissue, hepatic fatty acid uptake, peripheral lipolysis, β-oxidation, in silico model, we calibrate MINGLeD to the in vivo data of the different metabolic snapshots. The experimentally measured metabolites are closely related to many of the variables in the computational model, such that an identifiable model is achieved of which the model parameters can be determined using parameter estimation. For each of the diet cohorts, MINGLeD is fitted separately to the phenotype snapshot determined at each month during the dietary induction period. For each snapshot, we compute the average and standard deviation of the measured data at this time point and use this data to fit the model to using maximum likelihood estimation. −1–101) to accommodate multi-start optimization. The implementation details can be found in To validate the proposed structure of the The next step in our systems approach is to couple the phenotype snapshots in time. Hereto we make use of the computational technique entitled ‘Analysis of Dynamic Adaptations of Parameter Trajectories’ (ADAPT) –38. By ea priori unknown which model parameters change with time, it is not possible to perform a dynamic simulation of the entire time span in one go. Therefore we discretize the time span into 90 segments, each representing one day. ADAPT interpolates between the individual snapshots in time  and simulates every day in between these time points. To facilitate this, some pre-processing steps are required. Since the quantitative experimental data is discrete and only available at four points in time, the data is interpolated using cubic smoothing splines to obtain continuous dynamic descriptions of the experimentally observed metabolite pools and fluxes. To account for experimental and biological uncertainties, a collection of 1,000 splines is calculated using a Monte Carlo approach: different random samples of the experimental data are generated assuming Gaussian distributions with means and standard deviations of the data. Subsequently, for each generated sample, a cubic smoothing spline is calculated. This bootstrapping approach yields samples of data replicates which will subsequently be utilized in parameter estimation [Since it is timation . By combThe system is first simulated for the phenotype prior to the dietary induction by optimization to the t = 0 data. For each step in time, the system is simulated using the final values of the model states of the previous time step as initial conditions. Since we consider the parameters to be time-varying, the model parameters are re-optimized for each time step by minimizing the difference between the (sampled and interpolated) experimental data and the corresponding model outputs. The estimated parameter set from the previous time point is used as initial set for the optimization procedure. It is assumed that the induced adaptations are minimal and proceed progressively in time. Therefore, highly fluctuating parameter trajectories are considered to be non-physiological. To prevent the occurrence of such behavior, the parameter estimation protocol is extended to prevent unnecessary change of parameters and to identify minimal parameter adaptations that are required to describe phenotype transition. The cost function is extended with a regularization term .All simulation code and ADAPT yields a collection of parameter sets that describe the dynamics of the onset and development of MetS over time. The obtained trajectories for the model parameters, but also for the fluxes and pool sizes provide insight in the affected underlying biological system. This provides information about the adaptations that have taken place during the dietary induction, and these model-based predictions are compared to the gene expression data that is measured at the end of the dietary induction study.S1 FigPanels a-b display the dynamics in metabolite pools over time and panels e-t display the corresponding flux trajectories. We selected the n = 100 best trajectories (top 10% based on WSSE). The 10% range around the median trajectory is depicted by the shaded area and the median trajectory for each model component is depicted by the solid line for the low-fat diet group (light blue), high-fat diet group (dark blue), non-dyslipidemic Metabolic Syndrome phenotype (gray) and the dyslipidemic Metabolic Syndrome phenotype (red) respectively. Experimental data is represented by the black error bars (mean ± standard deviation).(PDF)Click here for additional data file.S1 Note(PDF)Click here for additional data file.S2 Note(PDF)Click here for additional data file.S3 Note(PDF)Click here for additional data file.S1 Data(XLSX)Click here for additional data file.


Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement.Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways.Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.The online version of this article (doi:10.1186/s12859-016-1412-z) contains supplementary material, which is available to authorized users. It follows r is a representative of [r] or that [r] is the coupling class of r. Note that [r]=[s] iff r⇔s. Biologically, coupling classes can be interpreted as subsets of reactions that are always active together at steady-state, similarly to the notion of enzyme subsets in  instead of having binary variables for each individual reaction. Thus we can rewrite the algorithm minNW in the following way: Based on the equivalence relation r]| denotes the cardinality of the coupling class [r]. Thus, we compute the smallest subnetwork with respect to the number of active reactions and not with respect to to the number of active representatives. Here, |[To exclude previously enumerated subnetworks the constraints  can be aUsing representatives we need only mentclass2pt{minimrep, we computed the coupling classes for partially coupled reactions using the software F2C2 [We implemented our MILPs in MATLAB and used CPLEX  as a solare F2C2 .Indicator variablesbig M constraints from the original MILP formulation in the big M constraint δa≤v≤Ma is replaced by a=0⇒v=0,a=1⇒v≥δ, where a∈{0,1} is the indicator variable. MILP solvers using indicator variables handle them in two different ways. They may reformulate the given indicator constraints into big M constraints or branch on the indicator variables. CPLEX chooses one of these two methods depending on M. If M is small, it will formulate big M constraints, otherwise it will use branching. For the results and the running time we only applied the version where indicator variables were used, due to numerical instability of the big M formulation. While indicator variables drastically increase the running time, we still outperform the algorithm in [We implemented two versions of our algorithms. In one version we used the rithm in .In a first experiment, we ran our implementations on the two metabolic network reconstructions and functionalities considered in . Table 2Synechocystis sp. PCC 6803, the subnetwork computed by NetworkReducer [For kReducer  containsE. coli iAF1260 we get similar results. The subnetwork computed by NetworkReducer contains 39 reactions more than the minimum subnetwork obtained by our method. Both networks have 424 reactions in common. There are 51 reactions that can only be found in the subnetwork computed with NetworkReducer, while there are 12 reactions which appear only in the minimum subnetwork.Regarding FASTCORE  is a heuH. pylori 26695 there are 22 reactions that appear only in the FASTCORE subnetwork and 9 reactions which can be found only in the minimum subnetwork. Similarly, for M. tuberculosis iNJ661, there are 78 reactions that appear only in the FASTCORE subnetwork and 6 reactions which can be found only in our subnetwork. The names of the reactions for both examples are given in the , SUCFUMt, L-alanine dehydrogenase, Anthranilate synthase, Formate-tetrahydrofolate ligase, D-Alanine exchange, D-alanine transport via proton symport, L alanine reversible transport via proton symport, L-Alanine exchange, ANS2, GAR transformylase-T, NO3t2, NO3t3, Catalase. Figure In total we computed 16 subnetworks each containing 321 reactions, which is the minimum number needed to fulfill the requirements. The time needed to compute all these minimum subnetworks was 127 seconds with minNW and 33 seconds with minNWAdditional insight can be obtained by analyzing co-occurrence patterns of the 18 non-essential reactions. Some of these reactions are mutually exclusive regarding the minimum subnetworks. For example, all subnetworks that contain reaction CCP do not contain CAT and vice versa. The same holds for the pair FTHFLi and GART, and the pair ANS and ANS2. Regarding the functionalities of these reaction pairs, one can easily check that the two reactions in each pair do basically the same. Therefore, it is sufficient if only one of them is present. In opposite to this, we can see that DALAt2r and EX_ala__D(e) form a cycle since they always appear in the same subnetworks. The same holds for ALAt2r and EX_ala__L(e). Both cycles also seem to be mutually exclusive, thus only one of them is present in the subnetworks. Similar observations can be made for the cycle formed by NO3t2 and NO3t3, which is mutually exclusive to the cycle formed by SUCFUMt and FUMt3.One may ask whether the reactions that never appear together in the same subnetwork are also mutually exclusive regarding elementary flux modes (EFMs), i.e., whether or not there exists an EFM involving both reactions . While tWe developed an MILP approach to compute for a given large metabolic network one or more minimum subnetworks preserving biological requirements that can be specified by the user. Compared to previous work , 8, 9, oOnce these subnetworks have been computed, further analysis becomes possible by using methods that are not applicable to the original network. For example, one may compute elementary flux modes and minimal cut sets. In addition, one can take a closer look to the reactions involved in one or all minimum subnetworks in order to get a better understanding of their role in the network.


Saccharomyces cerevisiae. IDREAM models contain many fewer interactions than PROM and yet produce significantly more accurate growth predictions. IDREAM consistently outperformed PROM using any of three popular yeast metabolic models and across three experimental growth conditions. Importantly, IDREAM’s enhanced accuracy makes it possible to identify subtle synthetic growth defects. With experimental validation, these novel genetic interactions involving the pyruvate dehydrogenase complex suggested a new role for fatty acid-responsive factor Oaf1 in regulating acetyl-CoA production in glucose grown cells.Gene regulatory and metabolic network models have been used successfully in many organisms, but inherent differences between them make networks difficult to integrate. Probabilistic Regulation Of Metabolism (PROM) provides a partial solution, but it does not incorporate network inference and underperforms in eukaryotes. We present an Integrated Deduced And Metabolism (IDREAM) method that combines statistically inferred Environment and Gene Regulatory Influence Network (EGRIN) models with the PROM framework to create enhanced metabolic-regulatory network models. We used IDREAM to predict phenotypes and genetic interactions between transcription factors and genes encoding metabolic activities in the eukaryote,  S. cerevisiae model with a PROM model using a TRN available from the YEASTRACT database. IDREAM outperforms PROM using any of three popular yeast metabolic models and across three experimental growth conditions, making it possible to identify subtle synthetic growth defects, and a new role for Oaf1 in the regulation of acetyl-CoA biosynthesis.The integration of gene regulatory and metabolic network models is an important goal in computational biology, in order to develop methods that can identify the underlying mechanistic links in biological networks and advance metabolic engineering techniques. In this paper, we develop a framework called Integrated Deduced REgulation And Metabolism (IDREAM) that can improve our ability to predict phenotypes of microorganisms, and particularly it can address the challenges in evaluating phenotypic consequence of perturbing transcriptional regulation of metabolism in a eukaryotic cell. We compare the predictive performance of an IDREAM  A major goal of systems biology is to predict the phenotypic consequences of environmental and genetic perturbations. Metabolism is a fundamental cellular system that strongly influences cell fate, and as such it is important to study the behavior and regulation of metabolic and to build models that integrate its functions with other cellular systems. Despite extensive study of the biochemistry and enzymology of metabolism for over a century, our ability to simulate the functions of metabolic networks and their interactions is still limited by their size and complexity, including their nonlinear dynamic behavior , 2. TradConstraint-based modeling techniques , 8 were FBA is a powerful method for phenotype prediction due to its ability to describe stoichiometrically determined levels of substrate consumption and product production for reactions in very large metabolic systems in the absence of kinetic information or enzyme concentrations. However, one of its main drawbacks is that it does not incorporate constraints imposed upon the network by regulation of gene expression. In fact, metabolic networks are dramatically affected by complex transcriptional regulatory networks . Changes in transcriptional regulation in response to environmental cues lead to changes in enzyme abundance or activity, which in turn lead to changes in physiological states and growth. Incorporating information about how metabolic genes are differentially regulated to metabolic network models may improve the predictions made by constraint-based analysis. The ability to integrate computational models of transcriptional regulation with models of metabolism would allow us to better describe the impact of mutations and environmental perturbations on functional metabolism. Such integrated models would have the potential to guide rational rewiring of metabolic flux and addition of new metabolic capabilities into a network , 17.A common strategy for incorporating gene regulatory information into metabolic network models is to use gene expression information to impose condition-specific flux constraints on the metabolic model. This strategy depends upon the assumption that elevated gene expression measurements make it more likely that there is increased activity for the metabolic enzymes encoded by the genes with increased expression, while lower gene expression levels are more likely to correspond to lower activity of the corresponding metabolic enzymes. Methods that impose condition-specific flux constraints on metabolic network models based upon gene expression data include GIMME , iMAT 1, E-Flux In previous work, some of us developed the Probabilistic Regulation of Metabolism (PROM) method for integrating transcriptional regulatory networks (TRNs) and metabolic networks , 30. In The genome-scale reconstruction of the metabolic network of the organism. The simulation of the metabolic network within the PROM method is performed using FBA subject to additional constraints and a penalty function.A regulatory network structure, which consists of a list of transcription factors, the targets of these transcription factors, and their interactions. These transcriptional regulatory networks have generally been constructed based on high-throughput protein—DNA interaction data and/or statistical inference of functional relationships from genomic and transcriptomic data.A collection of gene expression data measured under different conditions, which will allow the observation of various phenotypes for the organism under study.Escherichia coli and Mycobacterium tuberculosis , a , a 52], ement by . A true Experimentally determined yeast growth rates that have been normalized to wild-type growth rates  were comSynthetic lethality or sickness occurs when the combination of two gene deletion results in reduced fitness and can identify buffering relationships where one gene can compensate for the loss of another . We predSaccharomyces cerevisiae single deletion strains were from the yeast deletion haploid collection . All double deletion strains were haploids generated by mating corresponding single deletion strains from the same library or from the BY4741 collection (Invitrogen), followed by tetrad dissection and selection by G418 resistance and PCR.We validated the predicted synthetic lethal or sick pairs by experimental growth assay. ODELAY was used to provide objective measurements of yeast growth defects . Yeast sS1 FigA. The number of transcription factors in PROM and IDREAM. ‘Match_measuredTF’ is the number of TFs having a corresponding phenotype in Fendt’s experiment for 119 TF mutants. ‘Match_17defectTF’ is the number of TFs out of the 17 defect-inducing TFs that are involved in the two integrated models. B. The log value of number of regulatory interactions and metabolic genes in PROM and IDREAM.(PDF)Click here for additional data file.S2 FigAcross 16 different thresholds, the AUC value is significantly higher for IDREAM (mean = 0.67) than PROM (mean = 0.58).(PDF)Click here for additional data file.S3 FigThere are no significant differences by the three yeast models.(PDF)Click here for additional data file.S4 FigEach row represents a metabolic gene, and each column represents a gene encoding a TF.(PDF)Click here for additional data file.S5 FigEstimated doubling times inform a confidence score identifying double deletion strains with synthetic growth defects. The first columns shows the metric and plate, such that ‘Mean.1’ means that for replicate 1, the average growth rate of many colonies was estimated using the mean and ‘Geometric Mean.2’ means that for replicate 2, the average growth rate was calculated using the geometric mean. ‘# Exp’ and ‘# Control’ refers to the number of strains in the experiment and control sets (respectively) where the growth rate in the double deletion was significantly less than that expected by adding together the growth rates for single deletions. ‘Mean Exp’ and ‘Mean Control’ are the mean growth decrease in growth rate beyond that expected from adding together the single deletion decreases in growth rate for the experimental and control sets (respectively). ‘Fisher p-Val’ uses a Fisher’s exact test to compare the ‘# Exp’ to the ‘# Control’ while ‘T-test p-Val’ uses the measured magnitudes of the synergistic growth defects.(PNG)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLS)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S1 Script(ZIP)Click here for additional data file.S2 Script(ZIP)Click here for additional data file.


Pseudomonas aeruginosa UCBPP-PA14. We demonstrate how EnsembleFBA can be included in a systems biology workflow by predicting essential genes in six Streptococcus species and mapping the essential genes to small molecule ligands from DrugBank. We found that some metabolic subsystems contributed disproportionately to the set of predicted essential reactions in a way that was unique to each Streptococcus species, leading to species-specific outcomes from small molecule interactions. Through our analyses of P. aeruginosa and six Streptococci, we show that ensembles increase the quality of predictions without drastically increasing reconstruction time, thus making GENRE approaches more practical for applications which require predictions for many non-model organisms. All of our functions and accompanying example code are available in an open online repository.Genome-scale metabolic network reconstructions (GENREs) are repositories of knowledge about the metabolic processes that occur in an organism. GENREs have been used to discover and interpret metabolic functions, and to engineer novel network structures. A major barrier preventing more widespread use of GENREs, particularly to study non-model organisms, is the extensive time required to produce a high-quality GENRE. Many automated approaches have been developed which reduce this time requirement, but automatically-reconstructed draft GENREs still require curation before useful predictions can be made. We present a novel approach to the analysis of GENREs which improves the predictive capabilities of draft GENREs by representing many alternative network structures, all equally consistent with available data, and generating predictions from this ensemble. This ensemble approach is compatible with many reconstruction methods. We refer to this new approach as Ensemble Flux Balance Analysis (EnsembleFBA). We validate EnsembleFBA by predicting growth and gene essentiality in the model organism  Pseudomonas aeruginosa. We found that when predicting growth or essential genes, ensembles of GENREs achieved much better precision or captured many more essential genes than any of the individual GENREs within the ensemble. By improving the predictions that can be made with automatically-generated GENREs, this approach enables the modeling of biochemical systems which would otherwise be infeasible.Metabolism is the driving force behind all biological activity. Genome-scale metabolic network reconstructions (GENREs) are representations of metabolic systems that can be analyzed mathematically to make predictions about how a system will behave, as well as to design systems with new properties. GENREs have traditionally been reconstructed manually, which can require extensive time and effort. Recent software solutions automate the process  but the resulting GENREs are of lower quality and produce less reliable predictions than the manually-curated versions. We present a novel method (“EnsembleFBA”) which accounts for uncertainties involved in automated reconstruction by pooling many different draft GENREs together into an ensemble. We tested EnsembleFBA by predicting the growth and essential genes of the common pathogen  Metabolism is the driving force behind the wondrous flurry of biological activity carpeting our planet. An organism’s metabolism is determined by the metabolic enzymes encoded in its genome, the chemical reactions catalyzed by those enzymes, and whether or not those enzymes are actively expressed . The simGenome-scale metabolic network reconstructions (GENREs) are formal representations of metabolic networks . GENREs Many automated methods have been developed for rapidly reconstructing GENREs –16. We pPseudomonas aeruginosa, a well-studied, clinically-relevant pathogen. We provide an example workflow using EnsembleFBA by predicting gene essentiality in six Streptococcus species and mapping the predicted essential genes to small molecule ligands in DrugBank. All of our data and code are available in an online repository, including example scripts to simplify adoption of EnsembleFBA. Our ability to make mechanistic predictions about complex cellular communities requires advances in the way we leverage the data available to us, and the way we handle uncertainty. Ensemble FBA is a novel tool that maintains the speed of automated reconstruction methods while improving predictions by intentionally managing uncertainty in network structures.We begin by discussing a common GENRE curation procedure known as gap filling. We demonstrate that a global gap filling procedure  does not perform any better than a sequential one. Instead, we introduce an ensemble approach to pool the many possible network structures resulting from different sequences of the input media conditions . We demoGap filling is the process of identifying mismatches between computational predictions and experimental results, and identifying changes to the network structure which will bring the computational predictions into agreement with the experimental data. “Gaps” are missing reactions and can be filled by drawing from a database of possible metabolic reactions. Given that there are usually many mismatches between computational and experimental results, we demonstrate that simply changing the order in which computational results are brought into agreement with experimental data can result in different network structures. For example, suppose that it is experimentally determined that a microbe can grow on glucose minimal media and sucrose minimal media, but the computational predictions do not match. Gap filling the GENRE against a representation of glucose minimal media first and sucrose minimal media second, may result in a different network in the end than if gap filled against a representation of sucrose minimal media first. In practice, the order of gap filling is often arbitrary.Pseudomonas aeruginosa UCBPP-PA14 (without using the Model SEED gap filling feature). We gap filled this draft GENRE using 2, 5, 10, 15, 20, 25 and 30 media conditions that experimentally support growth. For each number of media conditions, the gap filling procedure was repeated 30 times. Each replicate consisted of drawing a random set of media conditions of the appropriate size, generating two random permutations of the drawn media conditions, gap filling in the order specified by those two permutations, and finally, comparing the resulting gap filled networks to each other. For example, for a single replicate of 5 media conditions, we selected five media conditions at random and selected two random permutations of these conditions . We gap filled twice, in the order prescribed by the two permutations, and compared the resulting networks. We repeated the process 30 times, each time drawing a new set of five random media conditions and gap filling using two random permutations of those five media conditions. We found that even with as few as two media conditions, gap filling in a different order resulted in an average of 25 unique reactions per GENRE . For each iteration , we randomly removed 20% of reactions from iPAU1129 and used the sequential and global approaches to gap fill from the universal database using a random selection of five media conditions. We chose to remove 20% of reactions to leave enough network context to constrain gap filling, as has been done previously [In order to determine whether the global solution was any more “biologically-relevant”, we also compared the ability of the global and sequential approaches to reconstruct a GENRE for eviously . The resBecause the sequential gap filling approach produces different results depending on the order of gap filling, we chose to maintain many possible structures resulting from random permutations of the input media conditions rather than select a single GENRE structure for downstream analysis . Not knowing the “true” network structure, we considered each different structure to be a “hypothesis” and analyzed them collectively. For each of 2 to 30 training media conditions we produced 21 GENREs by randomizing the gap fill order . We thenWe found that the “majority” threshold led the overall ensemble to achieve average accuracy with respect to the individual GENREs, consistently outperforming the least accurate of the individual GENREs . In order to span a greater range of potential GENRE structures, we added random weights (drawn from a uniform distribution) to the reactions in the gap filling step see . The ratP. aeruginosa UCBPP-PA14 included both positive (media conditions which supported growth) and negative results (media conditions which did not support growth). We formulated an iterative, optimization-based procedure which allowed us to incorporate information inherent in negative growth conditions into our automated curation  and running FBA. We compared the resulting gene essentiality predictions with experimental results [We evaluated the ability of ensembles to predict gene essentiality. We generated an ensemble of 51 GENREs, each created by gap filling with a random subset of 25 of the total 47 positive media conditions (53%), 10 randomly-selected negative media conditions from the total of 40 (25%), and 1,210 randomly-selected reactions from a total of 1,512 in the draft GENRE generated by Model SEED (80%). Genes were associated with reactions based on the assigned gene-protein-reaction (GPR) relationships from the draft GENRE. We used an  results . We founUsing the same ensemble of 51 GENREs from above, we examined the effect of ensemble size on predicting essential genes. We sampled with replacement 10,000 small ensembles from among the 51 GENREs for ensemble sizes of 2 through 51. We evaluated the accuracy, precision and recall against the same gene essentiality data set using the “any”, “majority”, and “consensus” thresholds. We found that for the “majority” threshold, smaller ensembles were less accurate, less precise, and more variable than larger ensembles . IncreasIn order to characterize the way gap filling distributes reactions throughout the ensemble, we generated an ensemble of 100 GENREs . Each GEStreptococcus which all have growth phenotype data available through a previous study [Streptococcus mitis, Streptococcus gallolyticus, Streptococcus oralis, Streptococcus equinus, Streptococcus pneumoniae and Streptococcus vestibularis . Many of these small molecules (113) interact with an essential gene in only one of the species, while 44 were predicted to target conserved essential genes in all six species . S. equiolecules . As an eS. mitis is predicted to have a greater proportion of essential reactions related to amino acid metabolism than other species, perhaps indicating that S. mitis has less redundancy in those pathways than the other six species. Essential reactions related to butanoate metabolism were most enriched in S. pneumoniae, while essential reactions in lysine degradation were most enriched in S. equinus. Interestingly, reactions associated with core metabolic functions  were not equally enriched among essential reactions for all species.To better understand the differences between the metabolic networks which underpin these small molecule screen results, we predicted reaction essentiality in rich media for all six species using a “majority” threshold. We found that several metabolic subsystems were enriched among essential reactions beyond what would be expected from random chance . Some suP. aeruginosa UCBPP-PA14 than the best individual GENREs. We showcase how EnsembleFBA can be utilized in a systems biology workflow by predicting how small molecules interact with different essential genes in six Streptococcus species. Ensembles increase the quality of predictions without incurring months of manual curation effort, thus making GENRE approaches more practical for applications which require predictions for many non-model organisms. We have provided code to facilitate the creation and analysis of ensembles of GENREs.Genome-scale metabolic network reconstructions (GENREs) have been used for decades to assemble information about an organism’s metabolism, to formally analyze that information, and in so doing, to make predictions about that organism’s behavior in unobserved or unobservable contexts. A major barrier preventing more widespread use of GENREs, particularly in non-model organisms, is the extensive time and effort required to produce a high-quality GENRE. Many automated approaches have been developed which reduce this time requirement  –15. We din silico on growth media which supports growth of the organism in vitro. Gap filling algorithms suggest parsimonious reaction sets from some “universal” biochemical database which, if added to a GENRE, will allow growth in the new environment [Gap filling is a common step during the GENRE curation process, both for manually- and automatically-curated GENREs . We usedironment ,17,18,23ironment . During A possible way around this issue of gap fill order is to remove the sequential nature of gap filling entirely and use a global gap filling approach. We demonstrate that not only is such a global approach much slower (quadratic increases in solution time as growth media conditions are added), but the solutions are no more parsimonious or biologically relevant . The redEnsembles have been used for many years in the machine learning community to leverage the strengths of many different models to improve predictions ,25. EnseEnsembles provide a significant advantage over individual GENREs by tuning for specific results with defined decision thresholds Figs  and 5. CWe observed that ensemble performance is limited by the quality of the GENREs which form the ensemble. The choice of decision threshold  did not drastically improve overall accuracy of the ensemble. However, by improving the individual GENREs using negative growth information, the overall ensemble accuracy improved dramatically . Also, iSeveral previous groups have developed methods for incorporating negative growth conditions into GENRE curation. The GrowMatch algorithm seeks to remove reactions in order to prevent growth in specific conditions . In thatIncreasing ensemble diversity impacted ensemble recall, but did not have an obvious effect on overall accuracy. Some degree of diversity is required in order to gain any advantage through an ensemble representation. In the “Order Only” ensemble  implementations of algorithms, Matlab simulation scripts, results files and figure generation scripts are publically available in our online repository:https://github.com/mbi2gs/ensembleFBAhttps://github.com/ModelSEED/ModelSEEDDatabase). The metabolic reaction and compound databases were parsed and formatted for use in Matlab using a custom Python script available in our repository (“format_SEED_data.py”). A draft network for P. aeruginosa UCBPP-PA14 was automatically generated using the Model SEED web service (http://modelseed.org/genomes/). Similarly, draft networks were generated for Streptococcus mitis ATCC 6249, Streptococcus gallolyticus ICDDRB-NRC-S3, Streptococcus oralis ATCC 49296, Streptococcus equinus AG46, Streptococcus pneumoniae (PATRIC ID 1313.5731), and Streptococcus vestibularis 22–06 S6.All biochemical reference data was obtained from the Model SEED database , and biomass representations were drawn from previous GENRE analyses of ruginosa ,34.P. aeruginosa PA14 essential genes in cystic fibrosis sputum medium were experimentally identified previously [eviously .P. aeruginosa UCBPP-PA14 called iPAU1129 was developed previously , along with Biolog growth screen data for P. aeruginosa UCBPP-PA14 indicating many media conditions in which this strain will and will not grow.A manually curated, and thoroughly validated GENRE of Streptococcus species was obtained from the file “Supplementary Data 1” of [http://www.drugbank.ca/) [Growth phenotype data for six ta 1” of . Small mank.ca/) . After iank.ca/) , we usedWe implemented a linear (as opposed to binary) gap filling algorithm in Matlab, based on the algorithms FASTGAPFILL and FastGapFilling ,18. We uU is the universal reaction library (as a stoichiometric matrix)X is the universal exchange library (same metabolites as U)u and Nx are the number of reactions in U and X, respectivelyNgc is the number of growth conditionsNngc is the number of non-growth conditionsNv is the vector of fluxes through Uw is the vector of fluxes through Xu,i, ubu,i, lbx,i, and ubx,i are the lower and upper bounds on vi and wi, respectivelylbbiomass,gc = j is the flux through the biomass reaction under growth condition jvzu,i and Czx,i are variables that can force reactions from U and X to be includedCz is a continuous variable which acts as a constraint on the absolute values of elements in v and w.r is an optional weight on z which can be randomizedIn order to incorporate genome annotations from a specific organism, we force the inclusion of all associated reactions from those annotations using the C variables. Note that unlike a binary optimization, the LP minimizing the sum of the absolute flux values through U and X does not necessarily result in a solution with the fewest reactions, but rather the solution which requires the minimum sum of the absolute values of the fluxes through it. The LP here can be extended to utilize multiple growth conditions simultaneously  by duplicating the U and X matrices, once for each growth condition, but minimizing a single set of z variables across all conditions. To gap fill using multiple growth conditions sequentially, we gap fill using the first growth condition, incorporate the solution into the GENRE, then repeat the process for all growth conditions. Our Matlab function “expand” implements this optimization problem.in silico data (negative growth conditions that erroneously predicted to support growth in silico). Having identified those, we then ran FBA on all the positive growth conditions to identify the top five with flux distributions most similar to the flux distribution of the negative growth condition. Flux distribution similarity was determined by calculating the Jaccard similarity between the reaction sets carrying non-zero flux values. Increasing the number of positive growth conditions increases compute time. The GENRE and the selected growth conditions are passed to the trimming problem, which takes the form:We implemented a binary optimization problem to trim a minimal set of reactions from a GENRE in order to prevent growth under negative growth conditions while simultaneously maintaining growth in the positive growth conditions. As input to the algorithm, we provide a GENRE, and a set of both positive and negative growth conditions. We chose to run FBA first to identify mismatches between the computational predictions and the U is the set of reactions from the GENRE (as a stoichiometric matrix)X is the set of exchange reactions from the GENRE (same metabolites as U)u and Nx are the number of reactions in U and X, respectivelyNgc is the number of growth conditionsNngc is the number of non-growth conditionsNv is the vector of fluxes through Uw is the vector of fluxes through Xu,i, ubu,i, lbx,i, and ubx,i are the lower and upper bounds on vi and wi, respectivelylbbiomass,gc = j is the flux through the biomass reaction under growth condition jvy is a set of binary variables which determine inclusion of reactions in the networkr is an optional weight on y which can be randomizedbiomass,ngc = j) = 0 requires the maximum flux through the biomass reaction for the non-growth conditions to be zero. In order to implement this constraint, we took advantage of duality theory as has been done previously [biomass,ngc = j) = 0 (constraint 10) with the following constraints:The term max. Similar constraints are produced for the product λlblb. The quadratic constraint above (constraint 11) can then be replaced by a linear constraint:Where tOur Matlab function “trim_active” implements this optimization problem.We implemented an iterative algorithm to integrate the LP expansion step with the binary trimming step. The algorithm first applies the expansion step to produce a GENRE that is capable of growing in all positive growth conditions. Next, the algorithm checks for negative growth conditions that allow for biomass flux and for any that do, applies the trim step as described above. The algorithm iterates between the expand and trim steps until either a completely consistent GENRE structure is identified, or it reaches a maximum attempts limit. A single attempt is completed if the GENRE structure is not yet consistent with the input growth conditions but stops making progress . In this case, a random reaction is removed from the GENRE and the search is re-initiated. If the maximum attempts limit is reached, the algorithm removes any negative growth conditions that are inconsistent with the positive growth conditions, and returns the final GENRE. This iterative algorithm is implemented in our Matlab function “build_network”.Growth media were simulated by setting the lower bounds on exchange reactions for the appropriate nutrients to negative values. The uptake of carbon source(s) limited the final flux through biomass. “Growth” was determined by maximizing flux through the biomass objective. We predicted “growth” if a positive, non-zero flux could be achieved through biomass. Gene knock-outs were simulated by generating a new GENRE which was missing the reactions dependent on the knocked-out gene. The reaction-gene dependence was determined by evaluating the binary logic of the GPRs provided by Model SEED. Our custom script to evaluate GPR logic is “simulateGeneDeletion”.We evaluated the growth predictions in terms of accuracy (TP + TN) / (TP + FP + TN + FN), precision (TP / TP + FP), and recall (TP / TP + FN) where TP = number of true positives, FP = the number of false positives, TN = the number of true negatives and FN = the number of false negatives. Precision indicates the fraction of positive predictions which are true positives. Recall indicates the fraction of positive events which were correctly predicted by the method.Streptococcus proteomes [We downloaded the Drug Target Sequences for small molecules in FASTA format from DrugBank . Using Nroteomes .Streptococcus species, we used the hypergeometric distribution to calculate the probability of drawing k essential reactions and finding that x or more are annotated with subsystem j, from a population of size M reactions, of which N are annotated with subsystem j.We downloaded KEGG subsystem annotations for the reactions in the Model SEED database (“KEGG.pathways.tsv”). After predicting essential reactions for each The majority of our reconstructions and simulations were performed on a 64-bit Dell Precision T3600 Desktop computer with 32 GB RAM and eight 3.6 GHz Intel Xeon CPUs, running Windows 7. Incorporating negative growth information often lead to longer reconstruction times (sometimes 2 hours per GENRE) due to the binary optimization step. To accelerate the reconstruction time while incorporating negative growth information, we used the University of Virginia’s high performance computing cluster.Our Matlab scripts for generating an ensemble (using the gap filling approach described in this work) and for analyzing an ensemble are freely available in a github repository (see Code and Data Availability). The Gurobi solver is required, in addition to our Matlab scripts. We have also included a tutorial script to guide the user through the necessary steps to generate and analyze an ensemble (“test_eFBA.mat”).S1 FigFor each number of media conditions, we generated 21 GENREs, where each GENRE was gap filled using a different order of the same input media conditions. Note that for two media conditions only two orders are possible. We evaluated the accuracy, precision, and recall of every individual GENRE and of the ensembles by predicting growth on 17 positive media conditions and 17 negative media conditions which were not used during gap filling. The average of the individual GENREs is shown as black points with the maxima and minima as black lines extended above and below. The ensemble predictions using the three different thresholds are shown as red circles “any”, green triangles “majority”, and blue squares “consensus”.(TIF)Click here for additional data file.S2 FigFor each number of media conditions, we generated 21 GENREs, where each GENRE was gap filled using a different order of the same input media conditions. Additional diversity was generated by using a stochastic gap fill step and including a random subset of the reactions from the Model SEED draft network. We evaluated the accuracy, precision, and recall of every individual GENRE and of the ensembles by predicting growth on 17 positive media conditions and 17 negative media conditions which were not used during gap filling. The average of the individual GENREs is shown as black points with the maxima and minima as black lines extended above and below. The ensemble predictions using the three different thresholds are shown as red circles “any”, green triangles “majority”, and blue squares “consensus”.(TIF)Click here for additional data file.S3 FigFor each number of media conditions, we generated 21 GENREs, where each GENRE was gap filled using a different order of the same input media conditions. Information about 10 randomly-selected negative growth conditions was incorporated through a trimming step. Additional diversity was generated by using a stochastic gap fill step and including a random subset of the reactions from the Model SEED draft network. We evaluated the accuracy, precision, and recall of every individual GENRE and of the ensembles by predicting growth on 17 positive media conditions and 17 negative media conditions which were not used during gap filling. The average of the individual GENREs is shown as black points with the maxima and minima as black lines extended above and below. The ensemble predictions using the three different thresholds are shown as red circles “any”, green triangles “majority”, and blue squares “consensus”.(TIF)Click here for additional data file.S4 FigEnsembles were assembled from networks which were trained with increasing fractions of the available data (from 0.2–1.0). For example, to create the individual networks in the ensemble at 0.2, we randomly selected 20% of the growth conditions and 20% of the non-growth conditions. Each individual network was gap filled on a new 20% subset of the data. The individual networks at 1.0 were all gap filled with all the data. The effects of gap filling with subsets of the data are threshold-dependent. We observed that for the “majority” threshold, increasing the fraction of data used to train individual networks increased accuracy and precision while slightly decreasing recall. For the “consensus” threshold, increasing the fraction of data had very little impact on accuracy or precision, but did increase recall. For the “any” threshold, increasing the fraction of data decreased accuracy and precision while improving recall.(TIF)Click here for additional data file.


Bioinformatics tools facilitate and accelerate all steps along the Design–Build–Test cycle of synthetic biology, for the enhanced production of natural products in engineered microbes. Covering: 2000 to 2016Progress in synthetic biology is enabled by powerful bioinformatics tools allowing the integration of the design, build and test stages of the biological engineering cycle. In this review we illustrate how this integration can be achieved, with a particular focus on natural products discovery and production. Bioinformatics tools for the DESIGN and BUILD stages include tools for the selection, synthesis, assembly and optimization of parts (enzymes and regulatory elements), devices (pathways) and systems (chassis). TEST tools include those for screening, identification and quantification of metabolites for rapid prototyping. The main advantages and limitations of these tools as well as their interoperability capabilities are highlighted. These compounds are used in a wide range of interesting applications, ranging from pharmaceutical uses as drugs against many diseases to flavours and fragrances in food and personal care products. Their economic potential and the fact that they are originally synthesized by biological systems make natural products highly attractive targets for the advanced genetic engineering strategies of synthetic biology, with the aim of producing them more efficiently, in more amenable host species, from cheaper raw material, and potentially with the option of introducing added value and new functionalities by engineered modifications of the biosynthetic pathways. The necessary large-scale engineering of microbial production systems is only possible if it is supported by tailored computational tools at each of the stages of the engineering cycle  to be added to engineered biosynthetic pathways.Computational design tools are needed in order to identify the best combinations of enzymes, pathways, regulatory components, and chassis organisms leading to the efficient production of target natural products see . This in5 For this approach to be successful, tools are needed to systematically search for all possible pathways leading to a target compound, and to correctly prioritize them through a ranking algorithm based on predicted pathway's efficiency. BNICE and SimZyme6 are a collection of pathway design tools that apply a set of reaction rules to predict possible biosynthetic routes towards desired target compounds and then identify the candidate enzymes that might be coerced to catalyse the necessary reactions. This tool kit has been applied to predict possible biosynthetic pathways for target compounds starting from native metabolites; these are currently awaiting experimental verification. Other recent proposed tools for selecting the most promising enzymatic route towards a target include the Sympheny Biopathway Predictor7 developed by Genomatica; RouteSearch,8 based on atom mapping; and PathPred,9 based on the reaction patterns in the KEGG database. Work in this area is still in a very early stage: for instance, PathPred was used to look for alternative biosynthesis routes in the flavonoid pathways converting the plant pigment delphinidin into gentiodelphin.9 The system was able to predict new pathways in addition to known pathways, but most of them were found to be non-viable upon manual inspection because they required predicted reactions that are chemically infeasible. The main challenge of pathway prediction tools will be the automated prioritization of successful candidates from among the easily generated thousands of alternative pathways. Possible criteria for identifying a predicted pathway as likely to be efficient are diverse and several computational approaches to estimate pathway efficiency have been proposed.10 For instance, Metabolic Tinker11 prioritizes pathways based on thermodynamic feasibility; FindPath12 in addition considers pathway length and theoretical yield; RetroPath/XTMS14 scores enzyme performance based on predicted promiscuous activities and adds toxicity of intermediates to the ranking; and GEM-Path15 includes flux efficiency.In an extreme variant of this approach, instead of modifying natural pathways, newly assembled enzymatic routes can be explored to produce a target natural product in a chassis organism.18 For the computational prediction of the properties of ribosome binding sites (RBS), the situation is slightly better, and there is a class of tools for engineering binding sites to achieve desired translation rates in prokaryotic hosts.22 Unlike other regulatory elements , RBS sites are strongly influenced by their flanking sequence, including the 5′ end of their cognate open reading frame (ORF) and, in operons, the 3′ terminus of the previous ORF.23 For this reason, the design of RBS sites should ideally be done simultaneously to ORF sequence optimization, but currently no tools are available to do this. So far, RBS prediction has been used successfully to debug aberrant RBS sites mid-ORF during sequence optimization,24 to design bespoke RBS,25 and to optimize RBS library design for the engineering of E. coli pathways to increase riboflavin levels26 and NADPH recycling.27An important consideration when designing an engineered pathway is the selection of regulatory components. Pathway efficiency requires preventing flux imbalances, which would lead to the depletion of essential precursors or the accumulation of intermediates, which in turn could result in toxicity or feedback inhibition of the pathway. This can be achieved by the right selection of regulatory components including promoters and transcriptional terminators, and ribosome binding site, which control transcription and translation rates, respectively. The accurate prediction of promoter and terminator properties is not currently possible based on sequence data alone; instead libraries of promoters and terminators have been experimentally characterised and standardised to allow predictive selection. The necessary characterisation information is held in databases such as The Registry of Standardised Biological Parts (http://parts.igem.org/Main_Page), and in the primary literature.28 can assist in the selection of the optimal chassis strain for a specific natural product,30 and the subsequent optimization of chassis metabolism. Central to in silico approaches for chassis selection and optimization are constraint-based flux prediction approaches.31 The first requirement for the application of these approaches is the availability of comprehensive descriptions of the stoichiometry of all metabolic reactions in an organism, which can usually be inferred from genome annotations in combination with manual curation. The resulting models collate all known metabolic reactions – along with information on metabolic enzymes, transporters, and their encoding genes – in a principled format that is amenable to computational analysis.32 Such models have increased in scale, coverage and quality over the last 15 years and are now available for many organisms relevant to industrial biotechnology.34 Furthermore, protocols and automated computational pipelines for their construction have been published.37 To select suitable chassis strains for a particular natural product, the reactions of its biosynthetic pathway are added to the metabolic models of a collection of different potential hosts, and multi-objective optimization  is applied to predict which strain can achieve the optimal balance between biomass production and the production of the desired chemical.Generally, natural products of interest are not naturally produced by common industrial production microbes; instead their biosynthetic pathways need to be engineered for recombinant production in industry-compatible strains. A growing number of genome-scale metabolic models (GEMs), available at the BioModels repository,38 Constraint-based flux analysis can be used to predict which genes will be the most promising targets for this strategy, and a large number of tools have been developed to implement this approach.43Even when a predicted optimal strain has been chosen for the engineered production of a natural product, additional rounds of strain optimization are usually required to reach industrially viable production levels. For this task, the same constraint-based metabolic models serve as the starting point. The basic premise of strain optimization is to amend host metabolism such that metabolic flux is increased towards the target molecule whilst maintaining cellular growth. This commonly involves the implementation of gene knockouts or over-expressions to channel metabolic flux as required.3et al.45). Furthermore, many commercial gene synthesis vendors  provide their own optimization algorithms for use prior to submitting orders, which allows further specific optimization for their synthesis methodology. All the available design tools allow codon optimization and the definition of specific base patterns such as restriction enzyme recognition sequences that should be avoided, but the rationale and algorithm for codon optimization and the degree of consideration of other criteria vary widely between programs.When introducing an engineered pathway into a new chassis strain, the applied genetic manipulations are no longer restricted to producing new combinations of selected pathway parts and regulatory elements. Instead, as DNA synthesis is increasingly affordable, it is possible to design the sequence of each individual part before combining them into optimized devices. At each step, multi-objective optimization is needed to ensure that synthetic genes express successfully in a given host, including organism-specific codon-optimization, alleviation of secondary mRNA structure, as well as removal of intrinsic regulation , repeating sequences and homopolymeric tracts. Many pieces of freely available software can be combined in automated pipelines for sequence optimization, as shown in 46 and the inclusion of unique ends facilitates seamless assembly methods such as Gibson and the Ligase Cycling Reaction.48 The process of defining the correct sequence for all parts and their intended combinations can be remarkably complex and error-prone, particularly when multiple or combinatorial assembly is to be performed. Design tools such as j5,49 SnapGene  and Genome Compiler  have functions for schematic in silico pathway construction, which will automatically generate the required oligomer sequences including restriction sites, overhangs and linkers. Furthermore, “recipes” – instructions for the experimental order of assembly of parts in vitro – are produced by these tools in order to streamline the sequence ordering and experimental process. These design tools have functionality to design assemblies compatible with such protocols as GoldenGate,46 InFusion , Gibson47 and Gateway cloning , and functionality is constantly improving to support new assembly methods.Individual DNA parts will be assembled into larger constructs to produce biosynthetic pathways, and so the design of the part sequences should be compatible with the downstream assembly method . For instance, removing all BsaI restriction sites makes parts compatible with GoldenGate assembly and variations,4de novo pathways require chemical transformations not necessarily seen in nature . In these instances, directed evolution can be employed to engineer enzymes to improve their activity towards a predetermined reaction.50 This method involves a close interaction of designing and building (and ultimately testing), which require special computational tools that allow this direct connection between the stages of the engineering cycle. Directed evolution approaches generate variant libraries of a gene of interest, encoding an enzyme that is predicted to have at least some activity towards the desired reaction, and selects variants that exhibit an improved function. Iterative cycles of variation and selection can be employed until the desired fitness  is reached. Traditionally, the necessary genetic diversity was achieved using random methods, primarily error-prone PCR53 or recombination,55 or site-directed mutagenesis (amongst others58). However, in the context of synthetic biology, gene synthesis59 approaches provide a means by which more rational strategies of protein engineering can be employed.A particular challenge for the engineering of natural products production involves those cases, where no suitable enzymes are available for a specific step within a pathway. This can be the case when the native enzyme that performs a particular transformation has not yet been identified, or when 61 and MUSCLE,62 can analyse patterns of sequence diversity and conservation within classes of proteins, which can inform about the site and type of mutations that are most likely to lead to improved functionality. If a 3D structure of the protein that serves as the evolutionary starting point is known, then the HotSpot Wizard tool,63 which integrates functional, structural and evolutionary data, can be used to identify potential target residues.Sequence alignment tools like Clustal50 the design tool GeneGenie64 can be used to guide the de novo synthesis of variant libraries. GeneGenie designs DNA sequences optimized for expression in a desired host, includes any sequences required for downstream cloning, and the mixed-base codon sequences. The resulting oligonucleotide sequences can then be synthesised and assembled using the SpeedyGenes method,59 which accommodates multiple and combinatorial variant sequences while at the same time implementing efficient enzymatic error correction, to create large but controlled libraries of variants, significantly reducing the “hands-on” time required for the experimental design.Having decided upon the target residues and type of variants to create,565 accumulation of unwanted intermediates, as well as unexpected pleiotropic consequences of the genetic manipulations. When focusing on quantitative profiling of changes in the composition of the growth medium , metabolomics can also provide highly useful flux constraints to include in genome-scale metabolic models, which increases their predictive power for improved strain designs. The models can be further supplemented by constraints based on quantitative transcriptome profiles, which in microbes can serve as an informative proxy for enzyme activity levels and thus pathway flux.66Following the construction of engineered microbial strains for natural product production, it is essential to characterize their phenotype in sufficient detail to provide informative feedback for the next iteration of the DESIGN stage. The major technological platform for this purpose are various molecular profiling methods, most importantly metabolomics. These methods not only help to characterize the production level of the target compound, but also allow a broad untargeted characterization of the metabolic state of the engineered microbe, which allows the detection of pathway bottlenecks,The development of computational tools for untargeted metabolomics is a mature area of research, and a large number of comprehensive software platforms have been made available in recent years . However674 or trackable gene traits,75 is necessary. Protocol languages for the automation of synthetic biology robotic platforms,76 such as the ones established by bio-foundries like Abolis, Zymergen, Ginkgo Bioworks, Amyris and SYNBIOCHEM, should facilitate the generalization of these pipelines. Moreover, integration of automated data analysis and machine-learning workflows into the protocols will ultimately provide the tools to seamlessly feed back from TEST into DESIGN.77 An area where rapid progress can be expected is the field of directed evolution for parts optimization; here, substantial datasets comprising quantitative sequence–activity information can often be obtained. In these cases, computational approaches, such as those implemented in the ProSAR software, can be adopted to infer predictive statistical models of sequence–activity relationships, to guide the next round of library design.80 Future improvements could include a more efficient mapping of an enzyme fitness landscape using machine learning algorithms, as has already been demonstrated in a related proof-of-concept for learning the sequence–activity relationship of DNA aptamers, using the Closed Loop Aptameric Directed Evolution (CLADE) approach.81Computational tools to automate the feedback from the molecular characterization of engineered strains in the TEST stage to the improved engineering strategies of the DESIGN stage are one of the major remaining gaps in the computational synthetic biology toolbox. Few convincing examples exist at the moment, and even when computational tools are used, these tend to be bespoke scripts for a specific project, rather than generalized pipelines. Existing design tools still require a better coupling to screening and selection technologies. The development of high-throughput approaches to that end, including targeted biosensors782 Of particular prominence for the establishment of computational standards is the Synthetic Biology Open Language (SBOL),83 an RDF-based standard for representing synthetic gene design that has been developed by an international consortium over recent years. The current release, SBOL v2.0,84 incorporates both structural and functional design features and integrates with systems biology modelling standards such as the Systems Biology Markup Language (SBML),85 providing a link between computational modelling (DESIGN) and wet-lab assembly (BUILD). SBOL is augmented with a visual representation, SBOL Visual86 which has the goal of standardising the visual representation of synthetic gene constructs, analogous to the standard representation of electronic circuits that enables electronic engineering. Moreover, optimization of the design process requires a better definition of constraints and objectives in a multiscale fashion. Such approaches would need to be matched by rapid prototyping systems for the BUILD stage exploring the design space efficiently. Similarly, autonomous and continuous learning from experimental test results needs to be enabled. Recently established bio-foundries, which are synthetic biology-based chemical manufacturers operating under tight and demanding constraints, serve as a critical testbed for computational tools at every step of the DESIGN–BUILD–TEST cycle and are key players in promoting the adoption of standard practices enabling software interoperability. It can be predicted that the experiences gained in these ambitious large-scale bio-engineering enterprises will rapidly diffuse to the wider synthetic biology community in the coming years.Efficient production of natural products in non-native chassis organisms is becoming more streamlined through the application of synthetic biology techniques. A growing range of computational tools is facilitating the synthetic biology engineering approach at each step of the process. However, the integration of DESIGN, BUILD and TEST tools is still one of the main challenges at present, and lack of interoperability between the bioinformatics tools is hindering a wider adoption of these tools by the community. Present requirements include a better standardisation to ensure interoperability between individual tools and seamless integration and traceability across the design/build/test stages. Several initiatives, like the NIST Synthetic Biology Standards Consortium, have recently been launched to address such standardisation issues.


Complex disorders including obesity, diabetes, fatty liver diseases, cardiovascular disease (CVD), and cancer are results from a combination of genetic, environmental, and lifestyle factors. The prevalence of such disorders has increased dramatically in the last two decades and there is an urgent need for the development of new prognostic tools for the treatment of such diseases. However, this requires a deep understanding of the underlying molecular mechanisms involved in the occurrence of the diseases. With the advances in high throughput technologies, biological components of cells can be measured with a very high resolution and these data can be used for investigating whole systems properties using a network-based approach. Systems medicine provides an integrative platform for studying the interactions between the biological components of the cell using a holistic approach and generating mechanistic explanations for the emergent systems properties  are important tools in systems biology and employed for simulating the metabolism of cells/tissues in different states  specific GEMs based on gene expression data and used their context-specific model to predict metabolic flux distributions in the brain tumor cells. The authors identified the GBM specific metabolic alterations and provided a comprehensive coverage of tumor metabolism. Moreover, flux distributions in glycolysis, glutaminolysis, TCA cycle, and lipid metabolism were predicted and validated by additional computational analysis and literature information.Tumor cells alter their metabolism to maintain their growth and proliferation. Zhang et al. evaluated the potential value of current major systems biology-based approaches, including genome wide association studies, gene regulatory networks, and protein–protein interaction networks and GEMs. The authors discussed how integrative analysis of personal multi-omics data may provide increased understanding of personal genotype–phenotype relationships. Moreover, the potential benefit of integrating different type of networks in increased understanding of the interactome is discussed. Recently, metabolic networks have been integrated with other biological networks and these networks have been used in the analysis if omics data obtained from different clinical conditions (Lee et al., Brown reviewed the challenges in the generation of SuperModels where computational models were integrated with various data types and analytics. The author has also discussed how these SuperModels may assist in the development of personalized and precision medicine.in vivo. Adiels et al. reviewed the recent kinetic studies and discussed how these studies may improve our understanding of impaired human lipoprotein metabolism. Even though, stable isotope labeling analyses have been highly targeted, in recent years, tools for the global non-targeted detection, quantification, and computational analysis of isotopic enrichment have become available. Weindl et al. discussed how such non-targeted stable isotope labeling analyses can be applied for systems medicine applications.Stable isotope assisted metabolomics techniques have been used in systems medicine for metabolic flux analysis and pathway discovery. It is essential to understand the pathophysiology of dyslipoproteinemia in humans since it has major role in the progression of complex diseases including CVD and diabetes. The use of tracers labeled with stable isotopes and mathematical modeling may provide a powerful tool for probing lipid and lipoprotein kinetics Shmelkov et al. described an approach to improve in silico identification of a comprehensive ensemble of targets for any drug weighted by the expression of those receptors in relevant tissues. Their approach may increase the sensitivity of target detection and allow for systematic integration of bioactivity/docking scores between drugs/compounds and proteins with the expression patterns of those proteins in human tissues.Finally, The work presented in this Research Topic addresses many of the recent progress in the applications of the GEMs is medical applications. The integration of GEMs with other biological networks and generation of whole cell models may foster the development of personalized medicine which may increase benefits and reduce risks for patients.AM and JN wrote the editorial together and approved its final version.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.