Patent Publication Number: US-2021192370-A1

Title: Identification and prediction of metabolic pathways from correlation-based metabolite networks

Description:
FIELD OF THE INVENTION 
     The present invention relates to the field of information technology adapted for modeling systems biology, and in particular for classifying metabolic pathways. 
     BACKGROUND 
     The identification and understanding of metabolic pathways is a key aspect of research in fields such as crop improvement and drug design. However, the identification of metabolic pathways (MPs) is a complex process based on a constraint-based, bottom-up approach; such identification typically uses gene annotation and ontology, computational derivation, and discrete manual curation. This process is described by Thiele and Palsson in “A protocol for generating a high-quality genome-scale metabolic reconstruction,”  Nature Protocols  5, 93-121 (2010). Manual curation typically requires a priori knowledge of the stoichiometry between compounds, thermodynamic information of the pathway&#39;s reactome, as well as its cellular compartmentalization, and other factors. Due to the complexity of the process, metabolic pathways and their regulating enzymes are often predicted based solely on gene ontology rather than on substantial experimental evidence. 
     The reconstruction of metabolic pathway networks follows a defined set of steps; initiated at the known biochemistry, genomics, and physiology, followed by the governing of the physico-chemical constraints, followed by flux distribution predictions, and finalized by the determination of which of the offered solutions translate into meaningful physiological states. Regardless of whether or not they are fully validated, MPs are represented in genome-scale databases, such as: PlantCyc (http://www.plantcyc.org), BioCyc (http://biocyc.org), KEGG (http://www.genome.jp/kegg). PlantCyc is a collection of metabolic pathways found in plants. TomatoCyc is a subset of PlantCyc containing metabolic pathways known to exist in tomato plants. Some additional metabolic pathways of tomato may be in PlantCyc, but have yet to be identified. Genome-scale MP databases capture substrate-product relationships. However, the schematically represented boundaries between series of biochemical reactions neglect the crosstalk and concerted regulation between biochemically distant pathways. Moreover, metabolic pathway networks are reconstructed based on the assumption of a condition-specific, steady-state metabolic flux distribution, as described by Monk, J., Nogales, J. &amp; Palsson, B. O., “Optimizing genome-scale network reconstructions,”  Nature Biotechnology  32, 447-452 (2014). This assumption does not account for endogenous or exogenous cues or factors, which may influence metabolic ties. 
     As opposed to the constraint-based approach of creating metabolic pathway networks, metabolite concentration correlation networks (CNs), also referred to herein simply as metabolite networks, provide a means for studying coordinated behavior of metabolites without the need for a priori knowledge. Profiles of metabolite concentrations are generated by high-throughput platforms, such as gas or liquid chromatography coupled to mass-spectrometry (GC, LC-MS), or nuclear magnetic resonance. The concentration profiles of multiple metabolites are correlated based on mathematically defined (dis-)similarity measures, which are subsequently transformed into a network form, where nodes represent the metabolites and the links between them the correlation coefficients. The usage of mathematically defined (dis-)similarity measures for metabolite correlation network analysis is described in Toubiana, et al., “Network analysis: tackling complex data to study plant metabolism,”  Trends in biotechnology  31, 29-36 (2013). The correlation coefficients generated and their corresponding p-values are subsequently subjected to threshold tests, removing spurious correlations. The remaining correlations are eventually transformed into network form, as described above. The resulting network illustrates a holistic view of metabolite relationships, reflecting the state of coordinated behavior at the time of sampling. For example, a correlation-based network (CN) approach was applied to metabolite concentration profiles of leaves of two grapevine cultivars to investigate the effects of different water stress regimes, as described by Hochberg, et al., “Metabolite profiling and network analysis reveal coordinated changes in grapevine water stress response,”  BMC Plant Biology,  13, 84, (2013). 
     Metabolite CNs are often reconstructed based on the exploitation of the natural variability of mapping populations or collections of different varieties or cultivars, as the multiple collections provide a large sample size, which stabilizes the correlation and reduces the error rate. CNs of metabolite concentration profiles can be combined with data of other cellular components as their relations are established based on (dis-)similarity measurements and not complex biological processes; an example is provided by Gibon, et al., “Integration of metabolite with transcript and enzyme activity profiling during diurnal cycles in  Arabidopsis  rosettes,”  Genome Biology  7(8):23 (2006), who studied metabolite data coupled with transcript and enzyme activity profiles to examine diurnal cycles in  Arabidopsis  rosettes. Structural properties of graphs can be used to interpret metabolite networks and to propose hypotheses. For instance, a network property analysis has been performed to identify loci regulating branched-chain amino acids in tomato seeds, as described in Toubiana, et al., “Combined correlation-based network and mQTL analyses efficiently identified loci for branched-chain amino acid, serine to threonine, and proline metabolism in tomato seeds,”  Plant Journal,  81(1):121-133 (2015). Community detection algorithms have also been applied to CNs to identify groups of nodes with similar chemical properties, referred to as modules, as described by Toubiana et al., “Trends in Biotechnology,” cited above. 
     SUMMARY 
     An aim of the present invention is to provide a system and method for identifying metabolic pathways from metabolite concentration correlation networks (CNs). Correlation-based network analysis (CNA) and machine learning methods were adapted to predict metabolic pathways in correlation networks created from metabolite profiles of the pericarp of a tomato introgression line population. The method maps existing metabolic pathways (MPs) onto a metabolite correlation network (CN), followed by computation of a set of network properties (i.e., features) for each pathway, so as to derive a machine learning model of metabolic pathway mapping. The resulting machine learning model is then used to predict the existence of previously unidentified metabolic pathways. 
     There is therefore provided, by embodiments of the present invention, a method for determining a likelihood of a metabolic pathway existing in an organism, implemented by a computer processor having an associated memory, the memory including instructions that when executed by the computer processor implement steps of the method including: calculating a pathway feature vector for each metabolic pathway of first and second sets of metabolic pathways; receiving the pathway feature vectors of the first and second sets of metabolic pathways at a supervised machine learning (SML) model to train the SML model for classifying metabolic pathways as existing or not existing in the organism; mapping a proposed metabolic pathway to the CN to determine a pathway feature vector of the proposed metabolic pathway; and processing the pathway feature vector of the proposed metabolic pathway, by the trained SML model (i.e., “feeding” the pathway feature vector of the proposed metabolic pathway to the trained SML model), to determine a likelihood of the proposed metabolic pathway existing in the organism. In some embodiments, the first set of metabolic pathways is composed of metabolic pathways known to exist in the organism, wherein the second set is composed of metabolic pathways not known to exist in the organism. Elements of the pathway feature vectors are network properties of the metabolic pathways mapped to a metabolite concentration correlation network (CN). The known pathway feature vectors indicate metabolic pathways existing in the organism and the unknown pathway feature vectors indicate pathways not existing in the organism. The proposed metabolic pathway is a metabolic pathway not known to exist in the organism. 
     In some embodiments, the method further includes setting a model threshold of the SML model, such that the likelihood of the proposed metabolic pathway existing in the organism is positive when the SML model indicates a prediction value above the threshold, and the likelihood is negative when the SML model indicates a prediction value below the threshold. 
     Further embodiments may include the additional step of performing in vivo testing of the proposed metabolic pathway when the likelihood of the proposed metabolic pathway existing in the organism is positive. 
     Training the SML model may also include training on at least two machine learning models and selecting a model that provides results having the greatest area under a receiver operating characteristic curve (AUC). The at least two machine learning models comprise at least one algorithm from a set including: random forest (RF), random forest with reduced feature set (RF red), AdaBoost (AB), XGBoost, random tree (RT), support vector machine (SVM), and naïve Bayes (nB) algorithms. 
     In further embodiments the pathway feature vectors include at least 20 of the features listed in Table 1 of the specification, hereinbelow. 
     Training the SML model may include applying the pathway feature vectors of the first and second sets of metabolic pathways to train a first SML model, determining a subset of features of the feature vectors that most contribute to the classifying capability of the first SML model, and training a second SML model by applying pathway feature vectors of the first and second sets that include only the subset of features determined to contribute the most to the classifying capability. In some embodiments, the subset of features are the features listed in Table 2 of the specification, hereinbelow. 
     In embodiments of the present invention, there is further provided a system for identifying previously unknown metabolic pathways in an organism, comprising a computer processor and an associated memory, the memory comprising instructions that when executed by the computer processor implement steps including: calculating a pathway feature vector for each metabolic pathway of first and second sets of metabolic pathways; receiving the pathway feature vectors of the first and second sets of metabolic pathways at a supervised machine learning (SML) model to train the SML model for classifying metabolic pathways as existing or not existing in the organism; mapping a proposed metabolic pathway to the CN to determine a pathway feature vector of the proposed metabolic pathway; and processing the pathway feature vector of the proposed metabolic pathway, by the trained SML model, to determine a likelihood of the proposed metabolic pathway existing in the organism. In some embodiments, the first set of metabolic pathways is composed of metabolic pathways known to exist in the organism, wherein the second set is composed of metabolic pathways not known to exist in the organism. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       For a better understanding of various embodiments of the invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings. Structural details of the invention are shown to provide a fundamental understanding of the invention, the description, taken with the drawings, making apparent to those skilled in the art how the several forms of the invention may be embodied in practice. 
         FIG. 1  is a flow diagram, depicting a process of detecting unknown metabolic pathways, according to some embodiments of the present invention. 
         FIG. 2  is a network diagram, depicting a process of mapping metabolic pathways to a metabolite correlation network, according to some embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     A workflow of the methodology applied here is presented in  FIG. 1 , which shows a process  20  for detecting metabolic pathways previously not known to exist in an organism, according to some embodiments of the present invention. Methods described herein used supervised machine learning techniques combined with metabolite CNA. Being based on quantitative measurements of metabolites, the CNA approach effectively accounts for post-transcriptional and post-translational events, circumventing the need for gene data integration. The process disclosed herein was applied in the identification of metabolic pathways within the tomato pericarp, as described further hereinbelow. 
     Steps of the process  20  are as follows. A metabolite concentration CN is generated for a given organism (step  22 ). Next, known metabolic pathways for the organism are mapped to the CN, to create a set of “positive” CN subgraphs, and a set of metabolic pathways known to not be present in the organism, and/or random sets of metabolites, are mapped to the CN, to create a set of “negative” CN subgraphs (step  24 ). For each of the positive and negative instances of subgraphs, respective positive and negative vectors of network features are calculated (step  26 ). Network features are various features of network topology described further hereinbelow. In an application of the process describe below, feature vectors of the mapped metabolic pathways (also referred to herein as “pathway feature vectors”) were generated with 148 network features for each of three CN networks (i.e., 444 features in total). 
     Multiple supervised machine learning models are then trained on the positive and negative pathway feature vectors, and k-fold cross validation is applied to determine a “working model” that is best able to differentiate between the positive and negative instances (step  28 ). Given the working model, the vectors may also be refined to include only the features that contribute the most to classification. Finally, a new set of pathways (i.e., “proposed” pathways), which may come from metabolic pathway databases, are mapped onto the CN, followed by computation of the feature vectors for the proposed pathways (step  30 ). The resulting feature vectors of the proposed pathways are then processed by the working model to be classified as either positive or negative, by comparing the prediction value result providing by the working model to a given threshold level (step  32 ). Proposed metabolic pathways scoring a prediction value greater than the threshold were classified as positively predicted (i.e., likely to exist in the organism). The threshold may be set to indicate that metabolic pathways that are positively predicted warrant further in vivo testing to confirm the existence of the metabolic pathway in the target organism (step  34 ). 
     Process  20  was applied by the inventors in a study to identify previously unknown metabolic pathways in tomato pericarp. A machine learning model generated in the study (hereinbelow, the “tomato pericarp study”) identified metabolic pathways likely to exist in the tomato pericarp, including the following pathways: β-alanine-degradation-I, tryptophan-degradation-VII-via-indole-3-pyruvate (yet unknown in plants), β-alanine-biosynthesis-III, and melibiose degradation. The melibiose degradation pathway was identified, even though melibiose was NOT among the metabolites used to generate the CNs. In vivo assays validated the presence of the melibiose-degradation pathway in the tomato pericarp. 
     Details of the application of process  20 , in particular for the study of metabolic pathways in tomato pericarp, are described in the following sections. 
     Generation of Metabolite Concentration CNs 
     General principles of generating metabolite CNs, using a pipeline for CN construction, are described by Toubiana, et al., “Network analysis: tackling complex data to study plant metabolism,”  Trends in Biotechnology  31, 29-36, 2013 [Toubiana (2013)]. Metabolite CNs are represented as weighted networks G i =(V i ,E i ,w), where V i  is the set of nodes corresponding to metabolites found in the dataset of season i, E is the set of links between them, and link weights (w:E→R) correspond to the Pearson correlation coefficient. (Hereinbelow, the terms nodes and metabolites are used interchangeably.) 
     Metabolite concentration profiles from tomato pericarp, for three different harvesting seasons, were generated by Schauer, et al., “Comprehensive metabolic profiling and phenotyping of interspecific introgression lines for tomato improvement.” Toubiana, et al., “Metabolic profiling of a mapping population exposes new insights in the regulation of seed metabolism and seed, fruit, and plant relations,”  PLOS Genetics,  8, 3:e1002612, 2012 [Toubiana (2012)] constructed, for the three seasons analyzed by Schauer, weighted CNs, which were used in the application of the present invention described here. For the CNs constructed by Toubiana (2012), network links were weighted according to their correlation coefficient, allowing negative values. Spurious correlations, where |r|≤0.3 and p≥0.01, were removed. The CN for season I included 75 nodes, corresponding to the 75 metabolites, and 473 links; the CN for the season II was composed of 75 nodes and 869 links, while the CN for season III had 78 nodes and 338 links. A numeric feature profile was computed for each group of nodes in each CN, as described further hereinbelow. 
     Mapping Metabolic Pathways to CNs 
     In total, the three seasons and the corresponding CNs contained 109 different metabolites, i.e. nodes, while 52 common metabolites were contained in all three CNs. Out of the 589 MPs listed in TomatoCyc, 169 pathways were identified that shared at least two compounds with the 52 common metabolites. Each of these 169 pathways was mapped as a subgraph onto the three CNs. The mapping was partial in a sense that it omitted compounds from the pathways that were not found in the 52 common metabolites. The super-pathway of lysine, threonine, and methionine biosynthesis II, had 36% of its compounds within the networks, which resulted in the largest of all subgraphs. In total, 67 pathways were represented by exactly two compounds, while for three pathways all of their compounds were found in the CNs. 
     The same analysis was repeated for the remaining 625 non-tomato plant pathways, identifying 33 pathways that shared at least two compounds with the tomato metabolite CNs. For the non-plant MetaCyc pathways, 151 pathways were identified that shared at least two or more compounds with the CNs. In both cases (tomato and non-tomato MPs), the largest number of compounds shared with the CNs was 18. 
     For the pathways corresponding to the TomatoCyc dataset, the largest relative frequency of ˜25% was observed at approximately 40% coverage, while for the pathways corresponding to the remaining PlantCyc and MetaCyc datasets the peak was reached at approximately 20% relative coverage with ˜22% and ˜31% relative frequency, respectively. To compare the relative distributions of coverage, a two-sided Kolmogorov-Smirnov test was employed, revealing that the PlantCyc vis-à-vis the TomatoCyc distributions, and the PlantCyc vis-à-vis the MetaCyc distributions, were statistically equal (p-values 0.09681 and 0.09887 respectively), while the TomatoCyc vis-à-vis the MetaCyc distribution was significantly different (p-value 2.631e-06). 
     Calculating Vectors of Network Features 
     In order to develop a machine learning classifier to predict previously unidentified pathways, a set of 148 different features of network properties were defined (listed in Table 1, below). Network-based features reflect a range of topological aspects of the network, as described in the following paragraphs. 
     One group of features that may be incorporated in the features vectors are based on structural properties that quantify the importance of nodes and describe their location within the network. These features include: number of neighbors, weighted degree, closeness centrality, betweenness centrality, stress centrality, and clustering coefficient. The edge betweenness centrality was used to quantify the importance of links, as described in Newman, M. O. &amp; University Press,  Networks: An Introduction,  2009. Structural properties for quantifying the relations between node pairs were geodesic distance, Jaccard coefficient, preferential attachment score, and friends measure, as described in Fire, M. et al., “Computationally Efficient Link Prediction in a Variety of Social Networks,”  Acm Transactions on Intelligent Systems and Technology  5 (2013). All of these properties were aggregated to produce features based on the sum, the mean, and the three central moments. 
     Next, various community detection algorithms were applied to each CN, and features were computed based on the resulting communities (i.e., densely connected clusters of nodes). Community detection algorithms were described by Newman, M. E. J. &amp; Girvan, M, “Finding and evaluating community structure in networks,”  Physical Review E,  69 (2004). 
     A set of communities may be denoted as C i ={C i   1 , C i   2 , . . . , C i   k , . . . } where k is the index of a community in a CN of season i. A pathway j can be represented as a subset of metabolites in the CN of season i, denoted as S i   j ⊆V i . Dispersion of metabolites across the various clusters may indicate the existence or absence of the respective chemical reactions. Therefore, an additional feature included in the list of features is the ratio of the metabolites of a pathway co-residing in the largest community: MAX k {|C i   k  ∩S i   j |/|S i   j |}. 
     Next, structural features from the neighborhoods of each pathway were computed. A neighborhood of the node v in the CN for season i is denoted as: Γ i (v)={u: (v, u) ∈E i }. Note that Γ i (v) is the set of all metabolites that are significantly correlated with v. Various features from the neighborhoods of nodes in each pathway were computed as follows: 
     Intersection: I i   j =|∩ u∈S     i       j   Γ i (u)| 
     Union: U i   j =∪ u∈S     i       j   Γ i (u)| 
     Distinct neighborhoods: D i   j =|{u:∃ v∈S     i       j   ,u∈Γ i (v)⊆¬∃ v≠q∈S     i       j   ,u∈Γ i (q)}| 
     Mixed neighborhoods: M i   j =U i   j −I i   j −D i   j    
     The “distinct neighborhoods” feature accounts for all nodes that are significantly correlated to exactly one metabolite within a pathway j. The “mixed neighborhoods” feature accounts for all nodes that are significantly correlated to more than one metabolite within a pathway j, but not all of them. These two features are reminiscent of symmetric difference as defined in set theory. In fact, for two nodes, the “distinct neighborhoods” feature is equal to the size of the symmetric difference of their neighborhoods. However, for a larger number of nodes both features are different from the symmetric difference. 
     The complete list of 148 features is shown in Table 1, below. The three CNs examined (corresponding to the three harvesting seasons I, II, and III) exhibited different topologies and thus, different feature vectors. These vectors were combined into a single feature vector of 444 features (148×3 networks). 
     Mapping Metabolic Pathways to Metabolite Correlation Networks 
       FIG. 2  is a network diagram, schematically depicting a mapping process  200 . Process  200  indicates the format of implementing steps  24  and  30  of process  20 , described above with respect to  FIG. 1 . As indicated in the figure, metabolic pathways are mapped as subgraphs onto the CNs. In mapping, each metabolite of a given metabolic pathway is associated with the node position of the metabolite in the metabolite network. The network features of the resulting subgraph can then be calculated a feature vector of the subgraph, which is the pathway feature vector. 
     Two types of subgraphs may be considered: conjunctive subgraphs and extended subgraphs. Conjunctive subgraphs included all nodes in S i   j  and links between them, denoted as SG i   j =(S i   j ,{(u,v) ∈E i :u ∈S∧v ∈S}, w). Extended subgraphs included all nodes in S i   j  as well as all of their neighbors, denoted as ESG i   j =(V′,E′,w i ), where V′=∪ v∈S     i       j    Γ i (v) and E′={(u, v) ∈E i : u, v ∈V′}. Network features (diameter, diameter centrality, global clustering coefficient, assortativity, density) computed on these two types of subgraphs may be used to describe the pathways. In addition, all features related to the centrality of nodes and links may be computed on the conjunctive subgraph. 
     The dataset analyzed included 339 pathways mapped to the CNs, for which the 444 features were computed. A large number of features may impair the ability of a machine learning model to generalize beyond the data points used to produce it, a phenomenon known as overfitting. To avoid overfitting and to identify the most contributing features, we selected the features with the highest information gain. This procedure reduces the entropy of the class variable, after analyzing the value for a given feature, as described by Yang, Y. &amp; Pedersen, J. O., “Proceedings of ICML-97, 14th International Conference on Machine Learning,” (ed. D. H. Fisher) pp. 412-420 (1997). In the tomato plant study, an InfoGain algorithm was used to rank the contribution of the features to machine learning models. A reduced model, composed of the 20 most highest ranking features according to the InfoGain algorithm, was then used as the model to run predictions of subsequent analysis (see Table 2, below). Feature reduction was performed using the Weka software package (version 3.6.11), described by Hall, M. et al. The WEKA Data Mining Software: An Update.  SIGKDD Explorations  11 (2009). All of the features were computed using the igraph package34 and standard libraries in R 35 (statistics software available at: https://www.r-project.org/). 
     Generating and Validating Supervised Machine Learning Models 
     To identify a machine learning (ML) algorithm appropriate for classifying previously unidentified metabolic pathways in the target organism (i.e., tomato plant), several types of ML algorithms may be tested, such as: random forest (RF), random forest with reduced feature set (RF red), AdaBoost (AB), random tree (RT), support vector machine (SVM), and naïve Bayes (nB). ML algorithm tuning (also referred to as “hyper-parameter optimization”) was performed by a trial-and-error approach. 
     Given an instance whose class is unknown, a trained ML model assigns a probability of that instance being positive (a tomato pathway) or negative (a non-tomato pathway). If the probability of an instance having a positive class is above a predefined threshold, then the predicted class of that instance is positive. Standard performance metrics can be used to compare the predicted classes assigned to the pathways vs. their true classes, i.e., the true positive rate (TPR, recall), false positive rate (FPR), precision, and F-measure. In addition, the performance of ML models can be described by the receiver operating characteristic (ROC) curve, which is created by plotting the TPR as a function of the FPR at different threshold levels. An area under the ROC curve (AUC) of ‘1’ indicates a perfect classifier. The AUC measure of model performance is advantageous because it does not require specifying a threshold and it is independent of the proportion of positive and negative instances in the dataset. 
     Several procedures may be used to evaluate the ability of an ML model to predict the class of previously unseen instances. In the k-fold, cross-validation method, a dataset is divided into k subsets, each with the same number of instances. Each subset is then removed from the dataset in turn. An ML model is trained based on the remaining subsets. The trained model is applied to every instance in the removed subset, and the predicted class is recorded. After k iterations all instances in the dataset have been assigned a predicted class as opposed to their original true class. Cross-validation is typically used to prove the stability of a given ML algorithm and to assess whether or not the trained model is prone to overfitting. On the one hand, a larger number of folds results in a larger number of instances in the training set during each iteration and consequently renders more accurate models. On the other hand, a larger k requires training more ML models during the evaluation, which increases the computational resources required. 
     Due to the large number of ML algorithms evaluated for the tomato pericarp study, 10-fold cross-validation was used to select the best ML algorithm. Once the best ML algorithm was chosen, the number of folds was increased to the maximal possible value (339 pathways in our case) in order to obtain the most accurate in silico evaluation results. This special case of k-fold cross validation is known as leave-one-out cross-validation (LOOCV). 
     All ML modeling and testing was performed using Weka40 software, version 3.6.11. For the current study, the best model was achieved using the random forest algorithm and an equal distribution between MetaCyc and randomly engineered pathways. The random forest model was run with 100 trees, each constructed while considering nine random features, and an out-of-bag error of 0.1711. The random forest algorithm is an ensemble of generated decision trees for which the average prediction of the individual trees is produced. The random forest algorithm for all seasons combined rendered the best AUC result of all models, achieving an AUC of 0.932 (see Table 3, below). The model also had an accuracy of 83.78% (284 correctly vs. 55 incorrectly classified instances). 
     Out of the 589 TomatoCyc pathways investigated in this study, 169 pathways were identified within each of the three CNs. These pathways were used as the positive instances of the training set. 
     ML models perform best when they are trained using a balanced training set where there is an equal number of positive and negative instances. In order to tackle this bias “non-pathways” (i.e., randomly generated sets of 2-18 metabolites) were added to the dataset as negative instances. Therefore, all of the positive instances were used for training, along with 85 randomly selected MetaCyc pathways and the same number of randomly selected non-pathways. In total, 170 negative instances were produced. 
     Sensitivity analysis was performed on the selected ML model, where a subset with 80% of the training set instances was randomly chosen to recreate a model with identical settings. After each model generation, test set instances were subjected to prediction. This analysis was performed with 100 iterations, after which the corresponding average and variance values were computed. If the average value of the sensitivity test corresponded to the value of the original model (greater or smaller than the threshold), the prediction was considered valid. The variance values were used as an indicator of goodness of the prediction value. All but one prediction value yielded valid predictions. 
     Applying Selected Machine Learning Model 
     After validation, the feature vectors of the abovementioned 33 plant pathways (which shared at least two compounds with the tomato metabolite CNs), and the remaining 66 MetaCyc pathways that were not included in the training set, were classified by the trained ML model. Prediction values associated with these instances ranged from 0 to 1. The metabolic pathway corresponding to each feature vector was then classified (i.e., predicted) as either positive or negative, at a threshold level of 0.5. That is, unknown metabolic pathways scoring a prediction value greater than the threshold were classified as positively predicted (see Table 4, below). 
     In total, 22 pathways obtained a prediction value of 0.5 or greater. Of these pathways, six were associated with PlantCyc pathways and 16 with MetaCyc pathways. The β-alanine degradation I pathway achieved the highest prediction value of 0.89. For the PlantCyc pathways, the melibiose degradation pathway achieved the highest prediction value of 0.68. 
     While the inspection of the relative distribution of the 20 features revealed many differences between positively and negatively predicted metabolic pathways, three features emphasized the difference in particular: the edge betweenness community of subgraph of season II showed higher values for the majority of the positively predicted metabolic pathways, indicating a greater edge betweenness for their corresponding subgraphs; for the weighted standard deviation local clustering coefficient of subgraph within graph feature of season III positively predicted metabolic pathways demonstrated a normal distribution, while negatively predicted metabolic pathways showed a bimodal, left-skewed distribution, suggestive for a greater variety of the local clustering coefficient of subgraphs of non-tomato predicted pathways; the leading eigenvector community of subgraph of season I illustrated a left-skewed distribution for the positively predicted metabolic pathways, showing that they tend to group themselves following a leading eigenvector community. 
     Sensitivity analysis of the reduced feature model demonstrated that out of the 22 metabolic pathways with a prediction value≥0.5, only one metabolic pathway was misclassified, namely the MetaCyc listed superpathway of histidine, purine, and pyrimidine biosynthesis. Out of the 77 metabolic pathways with a prediction value&lt;0.5, 20.77% were misclassified. 
     In Vivo Pathway Verification 
     Frozen pericarp tissue powder was extracted in chloroform-methanol, and metabolites were quantified by gas chromatography-mass spectrometry (GC-MS) following a procedure optimized for tomato tissue, as described at Roessner-Tunali, U. et al., “Metabolic profiling of transgenic tomato plants overexpressing hexokinase reveals that the influence of hexose phosphorylation diminishes during fruit development,”  Plant Physiol.,  133(1), 84-99 (2003). Pure standard of melibiose (purchased from Sigma) was diluted in methanol and run in different quantities to build calibration curves. In the standard, two peaks were identified (1MEOX) (8TMS) main-product and by-product (C37H89NO11Si8) MW 948 RI 2837 and 2868 by library RT 41.8 and 42.1 min. Extract sample (300 μL) was injected (1 μL) with and without spiked-in standard. Identification and annotation of melibiose was achieved based on a comparison to an authentic standard. In addition, control samples with spiked-in non-labeled standards were also used to confirm coelution. Metabolite identity was further matched against publically available databases, in particular the Golm Metabolome Database for GC-MS reference data at http://gmd.mpimp-golm.mpg.de. A similar approach was followed for galactose and glucose. 
     In addition, PCR amplification was performed on tomato genes Solyc01g10680, Solyc12g006450, Solyc06g071640, Solyc01g088170, Solyc11g071600, and Solyc09g064430, in DNA extracted from tomato fruits. Amplicons are visible (M—1Kb+DNA ladder). These include: genes corresponding to β-alanine degradation I pathway; genes corresponding to the L-tryptophan degradation VII (via indole-3-pyrtuvate) MP; genes corresponding to the β-alanine biosynthesis III pathway. 
     It is to be understood that all or part of a process and of a system implementing the process of the present invention may be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. All or part of the process and system may be implemented as a computer program product, tangibly embodied in an information carrier, such as a machine-readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, such as a programmable processor, computer, or deployed to be executed on multiple computers at one website or distributed across multiple websites. Memory storage may also include multiple distributed memory units, including one or more types of storage media. Examples of storage media include, but are not limited to, magnetic media, optical media, and integrated circuits. A computer configured to implement the process may access, provide, transmit, receive, and modify information over wired or wireless networks. The computing may have one or more processors and one or more network interface modules. Processors may be configured as a multi-processing or distributed processing system. Network interface modules may control the sending and receiving of data packets over networks. 
     It is to be further understood that the scope of the present invention includes variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. 
     Tables 
       
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 148 Network Features of Feature Vector 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 1 
                 as sortativity subgraph 
               
               
                 2 
                 average absolute weighted degree 
               
               
                 3 
                 average absolute weighted degree graph 
               
               
                 4 
                 average closeness centrality graph subgraph 
               
               
                 5 
                 average closeness centrality subgraph 
               
               
                 6 
                 average degree 
               
               
                 7 
                 average degree graph 
               
               
                 8 
                 average edge betweenness subgraph 
               
               
                 9 
                 average geodesic distance graph 
               
               
                 10 
                 average geodesic distance subgraph 
               
               
                 11 
                 average jaccard coefficient 
               
               
                 12 
                 average local clustering coefficient subgraph 
               
               
                 13 
                 average local clustering coefficient subgraph graph 
               
               
                 14 
                 average node betweenness subgraph 
               
               
                 15 
                 average stress centrality 
               
               
                 16 
                 average weighted degree 
               
               
                 17 
                 average weighted degree graph 
               
               
                 18 
                 average weighted geodesic distance graph 
               
               
                 19 
                 average weighted geodesic distance subgraph 
               
               
                 20 
                 common neighborhood 
               
               
                 21 
                 density subgraph 
               
               
                 22 
                 diameter subgraph 
               
               
                 23 
                 diameter through subgraph 
               
               
                 24 
                 distinct neighborhood 
               
               
                 25 
                 edge betweenness community subgraph 
               
               
                 26 
                 edge betweenness community weighted subgraph 
               
               
                 27 
                 edge number 
               
               
                 28 
                 edge number graph 
               
               
                 29 
                 fast greedy community subgraph 
               
               
                 30 
                 fast greedy community weighted subgraph 
               
               
                 31 
                 friends measure graph average 
               
               
                 32 
                 friends measure graph kurtosis 
               
               
                 33 
                 friends measure graph sd 
               
               
                 34 
                 friends measure graph skewness 
               
               
                 35 
                 friends measure graph sum 
               
               
                 36 
                 friends measure subgraph average 
               
               
                 37 
                 friends measure subgraph sd 
               
               
                 38 
                 friends measure subgraph skewness 
               
               
                 39 
                 friends measure subgraph sum 
               
               
                 40 
                 friends mesure subgraph kurtosis 
               
               
                 41 
                 geodesic distance graph 
               
               
                 42 
                 geodesic distance subgraph 
               
               
                 43 
                 geodesic distance weighted graph 
               
               
                 44 
                 geodesic distance weighted subgraph 
               
               
                 45 
                 global clustering coefficient subgraph 
               
               
                 46 
                 group betweenness subgraph 
               
               
                 47 
                 jaccard coefficient 
               
               
                 48 
                 kurtosis absolute weighted degree 
               
               
                 49 
                 kurtosis absolute weighted degree graph 
               
               
                 50 
                 kurtosis closeness centrality graph subgraph 
               
               
                 51 
                 kurtosis degree 
               
               
                 52 
                 kurtosis degree graph 
               
               
                 53 
                 kurtosis edge betweenness subgraph 
               
               
                 54 
                 kurtosis geodesic distance graph 
               
               
                 55 
                 kurtosis geodesic distance subgraph 
               
               
                 56 
                 kurtosis jaccard coefficient 
               
               
                 57 
                 kurtosis local clustering coefficient subgraph 
               
               
                 58 
                 kurtosis local clustering coefficient subgraph graph 
               
               
                 59 
                 kurtosis node betweenness subgraph 
               
               
                 60 
                 kurtosis stress centrality 
               
               
                 61 
                 kurtosis weighted degree 
               
               
                 62 
                 kurtosis weighted degree graph 
               
               
                 63 
                 kurtosis weighted geodesic distance graph 
               
               
                 64 
                 kurtosis weighted geodesic distance subgraph 
               
               
                 65 
                 kurtsos cloeseness centrality subgraph 
               
               
                 66 
                 label propagation community subgraph 
               
               
                 67 
                 label propagation community weighted subgraph 
               
               
                 68 
                 leading eigentvector community subgraph 
               
               
                 69 
                 leading eigenvector community weighted subgraph 
               
               
                 70 
                 mixed neighborhood 
               
               
                 71 
                 multilevel community subgraph 
               
               
                 72 
                 multilevel community weighted subgraph 
               
               
                 73 
                 preferential attachment score 
               
               
                 74 
                 sd absolute weighted degree 
               
               
                 75 
                 sd absolute weighted degree graph 
               
               
                 76 
                 sd closeness centrality graph subgraph 
               
               
                 77 
                 sd closeness centrality subgraph 
               
               
                 78 
                 sd degree 
               
               
                 79 
                 sd degree graph 
               
               
                 80 
                 sd edge betweenness subgraph 
               
               
                 81 
                 sd geodesic distance graph 
               
               
                 82 
                 sd geodesic distance subgraph 
               
               
                 83 
                 sd jaccard coefficient 
               
               
                 84 
                 sd local clustering coefficient subgraph 
               
               
                 85 
                 sd local clustering coefficient subgraph graph 
               
               
                 86 
                 sd node betweenness subgraph 
               
               
                 87 
                 sd stress centrality 
               
               
                 88 
                 sd weighted degree 
               
               
                 89 
                 sd weighted degree graph 
               
               
                 90 
                 sd weighted geodesic distance graph 
               
               
                 91 
                 sd weighted geodesic distance subgraph 
               
               
                 92 
                 skewness absolute weighted degree 
               
               
                 93 
                 skewness absolute weighted degree graph 
               
               
                 94 
                 skewness closeness centrality graph subgraph 
               
               
                 95 
                 skewness closeness centrality subgraph 
               
               
                 96 
                 skewness degree 
               
               
                 97 
                 skewness degree graph 
               
               
                 98 
                 skewness edge betweenness subgraph 
               
               
                 99 
                 skewness geodesic distance graph 
               
               
                 100 
                 skewness geodesic distance subgraph 
               
               
                 101 
                 skewness jaccard coefficient 
               
               
                 102 
                 skewness local clustering coefficient subgraph 
               
               
                 103 
                 skewness local clustering coefficient subgraph graph 
               
               
                 104 
                 skewness node betweenness subgraph 
               
               
                 105 
                 skewness stress centrality 
               
               
                 106 
                 skewness weighted degree 
               
               
                 107 
                 skewness weighted degree graph 
               
               
                 108 
                 skewness weighted geodesic distance graph 
               
               
                 109 
                 skewness weighted geodesic distance subgraph 
               
               
                 110 
                 total absolute weighted degree 
               
               
                 111 
                 total absolute weighted degree graph 
               
               
                 112 
                 total weighted degree 
               
               
                 113 
                 total weighted degree graph 
               
               
                 114 
                 union of neighborhood 
               
               
                 115 
                 walktrap community subgraph 
               
               
                 116 
                 walktrap community weighted subgraph 
               
               
                 117 
                 weighted average closeness centrality graph subgraph 
               
               
                 118 
                 weighted average closeness centrality subgraph 
               
               
                 119 
                 weighted average edge betweeness subgraph 
               
               
                 120 
                 weighted average local clustering coefficient subgraph 
               
               
                 121 
                 weighted average local clustering coefficient subgraph graph 
               
               
                 122 
                 weighted average node betweenness subgraph 
               
               
                 123 
                 weighted average stress centrality 
               
               
                 124 
                 weighted diameter subgraph 
               
               
                 125 
                 weighted diameter through subgraph 
               
               
                 126 
                 weighted global clustering coefficient subgraph 
               
               
                 127 
                 weighted group betweenness subgraph 
               
               
                 128 
                 weighted kurtosis closeness centrality graph subgraph 
               
               
                 129 
                 weighted kurtosis closeness centrality subgraph 
               
               
                 130 
                 weighted kurtosis edge betweenness subgraph 
               
               
                 131 
                 weighted kurtosis local clustering coefficient subgraph 
               
               
                 132 
                 weighted kurtosis local clustering coefficient subgraph graph 
               
               
                 133 
                 weighted kurtosis node betweenness subgraph 
               
               
                 134 
                 weighted kurtosis stress centrality 
               
               
                 135 
                 weighted sd closeness centrality graph subgraph 
               
               
                 136 
                 weighted sd closeness centrality subgraph 
               
               
                 137 
                 weighted sd edge betweenness subgraph 
               
               
                 138 
                 weighted sd local clustering coefficient subgraph 
               
               
                 139 
                 weighted sd local clustering coefficient subgraph graph 
               
               
                 140 
                 weighted sd node betweenness subgraph 
               
               
                 141 
                 weighted sd stress centrality 
               
               
                 142 
                 weighted skewness closeness centrality graph subgraph 
               
               
                 143 
                 weighted skewness closeness centrality subgraph 
               
               
                 144 
                 weighted skewness edge betweenness subgraph 
               
               
                 145 
                 weighted skewness local clustering coefficient subgraph 
               
               
                 146 
                 weighted skewness local clustering coefficient subgraph graph 
               
               
                 147 
                 weighted skewness node betweenness subgraph 
               
               
                 148 
                 weighted skewness stress centrality 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 20 features with best predictive ability for study 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Mathematical  
               
               
                 Feature 
                 Season 
                 Definition 
                 moment 
               
               
                   
               
               
                 Skewness absolute 
                 II 
                 The absolute weighted node 
                 skewness 
               
               
                 weighted degree of 
                   
                 degree quantifies the absolute 
                   
               
               
                 graph 
                   
                 weight of all links incident on a 
                   
               
               
                 Kurtosis absolute 
                 II 
                 node. In case of correlation-based 
                 kurtosis 
               
               
                 weighted degree of 
                   
                 networks the weight of an link 
                   
               
               
                 graph 
                   
                 corresponds to the absolute 
                   
               
               
                 Absolute weighted 
                 II 
                 correlation coefficient. Here it 
                 — 
               
               
                 degree of graph 
                   
                 denotes all links within the 
                   
               
               
                 Standard deviation 
                 II 
                 subgraph and the links linking the  
                 standard 
               
               
                 of absolute weighted 
                   
                 nodes of the subgraph to the 
                 deviation 
               
               
                 degree of graph 
                   
                 remaining nodes of the graph 
                   
               
               
                 Total absolute 
                 II 
                   
                 Accumulative 
               
               
                 weighted degree of 
                   
                   
                 absolute 
               
               
                 graph 
                   
                   
                 weighted  
               
               
                   
                   
                   
                 degree 
               
               
                 Weighted standard 
                 II 
                 The weighted node betweenness 
                 Standard 
               
               
                 deviation node 
                   
                 centrality of a node i is given by 
                 deviation 
               
               
                 betweenness 
                   
                 the number of weighted geodesic 
                   
               
               
                 centrality of 
                   
                 distances between any two nodes 
                   
               
               
                 subgraph 
                   
                 that contain node i - here 
                   
               
               
                   
                   
                 delimited to the subgraph 
                   
               
               
                 Edge number of 
                 II 
                 Total amount of links incident on 
                 — 
               
               
                 graph 
                   
                 adjacent nodes of subgraph 
                   
               
               
                   
                   
                 including links to the nodes of the 
                   
               
               
                   
                   
                 remaining graph 
                   
               
               
                 Edge betweenness 
                 II 
                 The edge betweenness community 
                 — 
               
               
                 community of 
                   
                 detecting algorithm is based on 
                   
               
               
                 subgraph 
                   
                 the edge betweenness centrality 
                   
               
               
                   
                   
                 property. It applies a hierarchical 
                   
               
               
                   
                   
                 decomposition process in which 
                   
               
               
                   
                   
                 links are removed based on their 
                   
               
               
                   
                   
                 betweenness score. Communities 
                   
               
               
                   
                   
                 are built based on the idea that 
                   
               
               
                   
                   
                 links connecting different 
                   
               
               
                   
                   
                 communities are more likely to be 
                   
               
               
                   
                   
                 contained as multiple shortest 
                   
               
               
                   
                   
                 paths. Here a feature is 
                   
               
               
                   
                   
                 constructed given by the ratio of 
                   
               
               
                   
                   
                 how many nodes of the subgraph 
                   
               
               
                   
                   
                 co-reside in the largest 
                   
               
               
                   
                   
                 community as opposed to nodes 
                   
               
               
                   
                   
                 that are located within other 
                   
               
               
                   
                   
                 communities. 
                   
               
               
                 Mixed 
                 II 
                 The mixed neighborhoods feature 
                 — 
               
               
                 neighborhoods 
                   
                 accounts for all nodes that are 
                   
               
               
                   
                   
                 significantly correlated to more 
                   
               
               
                   
                   
                 than one metabolite within a 
                   
               
               
                   
                   
                 pathway, but not all of them (see 
                   
               
               
                   
                   
                 definition in Materials and 
                   
               
               
                   
                   
                 Methods for more details) 
                   
               
               
                 Union of 
                 II 
                 The union of neighborhoods 
                 — 
               
               
                 neighborhoods 
                   
                 features quantifies how many 
                   
               
               
                   
                   
                 nodes/friends of order one all 
                   
               
               
                   
                   
                 nodes within the subgraph have in 
                   
               
               
                   
                   
                 total, counting each friend only 
                   
               
               
                   
                   
                 once in the background of the 
                   
               
               
                   
                   
                 entire graph and excluding 
                   
               
               
                   
                   
                 friendship to each other (see 
                   
               
               
                   
                   
                 definition in Materials and 
                   
               
               
                   
                   
                 Methods for more details) 
                   
               
               
                 Total weighted 
                 II 
                 The weighted degree quantifies 
                 Accumulative 
               
               
                 degree of graph 
                   
                 the weight of all links incident on 
                 weighted  
               
               
                   
                   
                 a node. In case of correlation- 
                 degree 
               
               
                   
                   
                 based networks the weight of a 
                   
               
               
                   
                   
                 link corresponds to the correlation 
                   
               
               
                   
                   
                 coefficient. Here it denotes all 
                   
               
               
                   
                   
                 links within the subgraph and the 
                   
               
               
                   
                   
                 links linking the nodes of the 
                   
               
               
                   
                   
                 subgraph to the remaining nodes 
                   
               
               
                   
                   
                 of the graph 
                   
               
               
                 Weighted average 
                 II 
                 The weighted closeness centrality 
                 Average 
               
               
                 closeness centrality 
                   
                 is the reciprocal of the weighted 
                   
               
               
                 of subgraph 
                   
                 average path length between a 
                   
               
               
                   
                   
                 given node i and all other nodes in 
                   
               
               
                   
                   
                 a given connected graph. Here, 
                   
               
               
                   
                   
                 the closeness centrality was 
                   
               
               
                   
                   
                 measured for every node in the 
                   
               
               
                   
                   
                 subgraph. 
                   
               
               
                 Average closeness 
                 III 
                 The closeness centrality is the 
                 Average 
               
               
                 centrality of 
                   
                 reciprocal of the average path 
                   
               
               
                 subgraph 
                   
                 length between a given node i and 
                   
               
               
                   
                   
                 all other nodes in a given 
                   
               
               
                   
                   
                 connected graph. Here, the 
                   
               
               
                   
                   
                 closeness centrality was measured 
                   
               
               
                   
                   
                 for every node in the subgraph. 
                   
               
               
                 Density of subgraph 
                 I 
                 The density of a graph is the 
                 — 
               
               
                   
                   
                 number of links over the number 
                   
               
               
                   
                   
                 of possible links - here delimited 
                   
               
               
                   
                   
                 to the subgraph 
                   
               
               
                 Average closeness 
                 I 
                 See above 
                 Average 
               
               
                 centrality of 
                   
                   
                   
               
               
                 subgraph 
                   
                   
                   
               
               
                 Weighted average 
                 I 
                 See above 
                 Average 
               
               
                 closeness centrality 
                   
                   
                   
               
               
                 of subgraph 
                   
                   
                   
               
               
                 Weighted standard 
                 III 
                 The local clustering coefficient of 
                 Standard 
               
               
                 deviation local 
                   
                 a node i is the proportion of 
                 deviation 
               
               
                 clustering 
                   
                 existing links from all possible 
                   
               
               
                 coefficient of 
                   
                 links between the neighbors of i, 
                   
               
               
                 subgraph within 
                   
                 taking into account the weight of 
                   
               
               
                 graph 
                   
                 edges. It quantifies how close the 
                   
               
               
                   
                   
                 subnetwork induced by i and its 
                   
               
               
                   
                   
                 adjacent nodes is from a clique. 
                   
               
               
                   
                   
                 Here, the local clustering 
                   
               
               
                   
                   
                 coefficient is estimated for all 
                   
               
               
                   
                   
                 nodes in the subgraph in the 
                   
               
               
                   
                   
                 background of the entire graph. 
                   
               
               
                 Leading eigenvector 
                 I 
                 The leading eigenvector 
                   
               
               
                 community of 
                   
                 community detecting algorithm 
                   
               
               
                 subgraph 
                   
                 applies a top-down hierarchical 
                   
               
               
                   
                   
                 approach that optimizes the 
                   
               
               
                   
                   
                 modularity function. In each step 
                   
               
               
                   
                   
                 the graph is split into two parts in 
                   
               
               
                   
                   
                 a way that separation yields a 
                   
               
               
                   
                   
                 significant increase in modularity. 
                   
               
               
                   
                   
                 The split is performed by 
                   
               
               
                   
                   
                 determining the leading 
                   
               
               
                   
                   
                 eigenvector of the so-called 
                   
               
               
                   
                   
                 modularity matrix. Here a feature 
                   
               
               
                   
                   
                 is constructed given by the ratio 
                   
               
               
                   
                   
                 of how many nodes of the 
                   
               
               
                   
                   
                 subgraph co-reside in the largest 
                   
               
               
                   
                   
                 community as opposed to nodes 
                   
               
               
                   
                   
                 that are located within other 
                   
               
               
                   
                   
                 communities. 
                   
               
               
                 Average closeness 
                 II 
                 See above 
                 Average 
               
               
                 centrality of 
                   
                   
                   
               
               
                 subgraph 
                   
                   
                   
               
               
                 Average weighted 
                 II 
                 See above 
                 Average 
               
               
                 degree of graph 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Random forest model performance measure summary 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 True 
                 False 
                   
                   
                   
               
               
                   
                   
                 positive 
                 positive 
                   
                   
                   
               
               
                   
                 Class 
                 rate (Recall) 
                 rate 
                 Precision 
                 F-Measure 
                 AUC 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 All Season 
                 TomatoCyc pathways 
                 0.917 
                 0.241 
                 0.791 
                 0.849 
                 0.932 
               
               
                 features- 
                 MetaCyc and random 
                 0.759 
                 0.083 
                 0.902 
                 0.824 
                 0.932 
               
               
                 model I 
                 pathways 
                   
                   
                   
                   
                   
               
               
                   
                 Weighted average 
                 0.838 
                 0.162 
                 0.847 
                 0.837 
                 0.932 
               
               
                 Season I 
                 TomatoCyc pathways 
                 0.864 
                 0.182 
                 0.825 
                 0.844 
                 0.918 
               
               
                 features- 
                 MetaCyc and random 
                 0.818 
                 0.136 
                 0.858 
                 0.837 
                 0.917 
               
               
                 Model II 
                 pathways 
                   
                   
                   
                   
                   
               
               
                   
                 Weighted average 
                 0.841 
                 0.159 
                 0.841 
                 0.841 
                 0.917 
               
               
                 Season II 
                 TomatoCyc pathways 
                 0.876 
                 0.229 
                 0.791 
                 0.831 
                 0.91 
               
               
                 features- 
                 MetaCyc and random 
                 0.771 
                 0.124 
                 0.862 
                 0.814 
                 0.91 
               
               
                 model III 
                 pathways 
                   
                   
                   
                   
                   
               
               
                   
                 Weighted average 
                 0.823 
                 0.177 
                 0.827 
                 0.823 
                 0.91 
               
               
                 Season III 
                 TomatoCyc pathways 
                 0.828 
                 0.306 
                 0.729 
                 0.776 
                 0.876 
               
               
                 features- 
                 MetaCyc and random 
                 0.694 
                 0.172 
                 0.803 
                 0.744 
                 0.876 
               
               
                 model IV 
                 pathways 
                   
                   
                   
                   
                   
               
               
                   
                 Weighted average 
                 0.761 
                 0.239 
                 0.766 
                 0.76 
                 0.876 
               
               
                 Averaged 
                 TomatoCyc pathways 
                 0.858 
                 0.212 
                 0.801 
                 0.829 
                 0.914 
               
               
                 seasons 
                 MetaCyc and random 
                 0.788 
                 0.142 
                 0.848 
                 0.817 
                 0.914 
               
               
                 feature- 
                 pathways 
                   
                   
                   
                   
                   
               
               
                 model V 
                 Weighted average 
                 0.823 
                 0.177 
                 0.825 
                 0.823 
                 0.914 
               
               
                 Reduced 
                 TomatoCyc pathways 
                 0.858 
                 0.188 
                 0.819 
                 0.838 
                 0.923 
               
               
                 features 
                 MetaCyc and random 
                 0.812 
                 0.142 
                 0.852 
                 0.831 
                 0.923 
               
               
                 based 
                 pathways 
                   
                   
                   
                   
                   
               
               
                 on model I- 
                 Weighted average 
                 0.835 
                 0.165 
                 0.836 
                 0.835 
                 0.923 
               
               
                 model VI 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Pathway existence prediction values, showing sensitivity analysis. A sensitivity 
               
               
                 analysis average of less than 0.5 is deemed false. All but one of the 22 PlantCyc positively 
               
               
                 predicted pathways were confirmed by sensitivity analysis. 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Conform to 
               
               
                   
                   
                   
                 Sensitivity 
                 Sensitivity 
                 original 
               
               
                   
                   
                 Original  
                 analysis 
                 analysis 
                 model  
               
               
                 Database 
                 Pathway 
                 model 
                 average 
                 variance 
                 average 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 MetaCyc 
                 beta-alanine degradation I 
                 0.89 
                 0.631 
                 0.01812 
                 TRUE 
               
               
                 MetaCyc 
                 superpathway of butirocin 
                 0.85 
                 0.914 
                 0.00990 
                 TRUE 
               
               
                   
                 biosynthesis 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 isopenicillin N biosynthesis 
                 0.85 
                 0.879 
                 0.01379 
                 TRUE 
               
               
                 MetaCyc 
                 L-tryptophan degradation VII  
                 0.76 
                 0.773 
                 0.01815 
                 TRUE 
               
               
                   
                 (via indole-3-pyruvate) 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 L-tryptophan degradation IV  
                 0.76 
                 0.843 
                 0.01298 
                 TRUE 
               
               
                   
                 (via indole-3-lactate) 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 gliotoxin biosynthesis 
                 0.75 
                 0.843 
                 0.01298 
                 TRUE 
               
               
                 MetaCyc 
                 superpathway of scopolin and 
                 0.71 
                 0.928 
                 0.00850 
                 TRUE 
               
               
                   
                 esculin biosynthesis 
                   
                   
                   
                   
               
               
                 PlantCyc 
                 melibiose degradation 
                 0.68 
                 0.534 
                 0.08974 
                 TRUE 
               
               
                 PlantCyc 
                 beta-alanine biosynthesis III 
                 0.68 
                 0.596 
                 0.03190 
                 TRUE 
               
               
                 MetaCyc 
                 apicidin F biosynthesis 
                 0.68 
                 0.862 
                 0.01167 
                 TRUE 
               
               
                 MetaCyc 
                 creatine biosynthesis 
                 0.68 
                 0.796 
                 0.02079 
                 TRUE 
               
               
                 MetaCyc 
                 mycolyl-arabinogalactan- 
                 0.65 
                 0.708 
                 0.02882 
                 TRUE 
               
               
                   
                 peptidoglycan complex 
                   
                   
                   
                   
               
               
                   
                 biosynthesis 
                   
                   
                   
                   
               
               
                 PlantCyc 
                 putrescine degradation I 
                 0.63 
                 0.749 
                 0.02393 
                 TRUE 
               
               
                 PlantCyc 
                 hypoglycin biosynthesis 
                 0.61 
                 0.824 
                 0.01497 
                 TRUE 
               
               
                 MetaCyc 
                 L-tryptophan degradation VIII  
                 0.61 
                 0.704 
                 0.02038 
                 TRUE 
               
               
                   
                 (to tryptophol) 
                   
                   
                   
                   
               
               
                 PlantCyc 
                 lathyrine biosynthesis 
                 0.6 
                 0.639 
                 0.02321 
                 TRUE 
               
               
                 MetaCyc 
                 superpathway of L-methionine 
                 0.6 
                 0.731 
                 0.02034 
                 TRUE 
               
               
                   
                 salvage and degradation 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 superpathway of histidine, purine, 
                 0.58 
                 0.481 
                 0.03771 
                 FALSE 
               
               
                   
                 and pyrimidine biosynthesis 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 L-glutamate degradation VIII (to 
                 0.54 
                 0.571 
                 0.03319 
                 TRUE 
               
               
                   
                 propanoate) 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 L-phenylalanine degradation IV 
                 0.53 
                 0.714 
                 0.02364 
                 TRUE 
               
               
                   
                 (mammalian, via side chain) 
                   
                   
                   
                   
               
               
                 PlantCyc 
                 superpathway of aspartate and 
                 0.52 
                 0.624 
                 0.02851 
                 TRUE 
               
               
                   
                 asparagine biosynthesis 
                   
                   
                   
                   
               
               
                 MetaCyc 
                 benzoate fermentation (to acetate 
                 0.5 
                 0.609 
                 0.03113 
                 TRUE 
               
               
                   
                 and cyclohexane carboxylate)