Now that the annotated metabolic pathways been organized into different categories according to their functions. For a new or unknown molecular, knowing which or what kind of pathways it belongs to can help to understand its metabolic mechanism, which is very useful for drug discovery. Therefore, the metabolic pathways prediction mentioned in this paper refers to identifying the metabolic pathways that a compound involves in. There have some machine learning methods been applied to building prediction models for pathways. For example, Baranwal et al. (2019) proposed a hybrid framework of random forest (RF) and a graph convolution neural network for predicting the classes of metabolic pathways that a compound belongs to. Their method can only identify metabolic pathway types of compounds rather than the actual metabolic pathways. There remains a gap between predicting the type of metabolic pathways and predicting actual metabolic pathways to which the compound belongs. To fill this gap, Jia et al. (2020) proposed a similarity-based model for predicting the metabolic pathways of given compounds. They regarded every pair of compound and metabolic pathway as a sample, and represented each sample by seven features extracted from seven associations of compounds. And then they built a binary classification model with the RF algorithm to output “yes” or “no” for every pair, where “yes” means the compound belongs to the pathway, and “no” for not. However, the method is only suitable for known pathways, and it is impossible to predict whether the compounds belong to unknown pathways. Moreover, just predicting metabolic pathways that given compounds belong to is not enough to fully understand their roles in the metabolism, and thus it is necessary to reconstruct or design the metabolic pathways involved by the compounds.

In metabolic engineering, one usually needs to design or find metabolic pathways to chemicals of interest that meets certain constraints in a strain from living organisms. In order to expand the chemical repertoire for the production of compounds, a major effort is required in the development of novel design tools that target chemical diversity through rapid and predictable protocols. Addressing that goal involves retrosynthesis approaches that explore the chemical biosynthetic space. The basic idea of a retrosynthesis approach is to iteratively break down a target molecule into simpler molecules that can be combined chemically or enzymatically to produce it until all required compounds are either commercially available or present in the microbial strain of choice (Koch et al., 2020). Several researchers have reviewed efforts of retrosynthesis (Planson et al., 2012; Wang et al., 2017; Lin et al., 2019). However, the complexity associated with the large combinatorial retrosynthesis design space has often been recognized as the main challenge hindering the approach (Delépine et al., 2018). Pathway pruning methods (Gerlee et al., 2009) or optimization-based (Küken and Nikoloski 2019; Koch et al. 2020) methods are usually used to explore the chemical biosynthetic space. For example, Connor et al. (2017) proposed a Retrosynthesis approach Based on Molecular Similarity; Delépine et al. (2018) developed an automated open source workflow for retrosynthesis based on generalized reaction rules that perform the retrosynthesis search from chassis to target through an efficient and well-controlled protocol; Koch et al. (2020) proposed to explore the bioretrosynthesis space using the Monte Carlo Tree Search reinforcement learning method, guided by chemical similarity. However, the integration of both metabolic engineers’ expertise and years of lessons from the industry is not enough when performing pathway searching and ranking, resulting that the designed pathway may be far from the optimal.

In order for the reconstruction of metabolic pathways, de novo reaction prediction is still a significant challenge. Though some methods can learn the enzymatic reaction likeness to predict whether a compound-compound pair is possible converted by an enzymatic reaction, and even can find hidden reactions among many compounds at a time, they are insufficient to predict a multistep metabolic pathway correctly.

In order to construct the metabolic pathways, more efforts should be paid for the difficulties of distinguishing unidentified parts of the pathways and structuring pathways for desired products. In particular, the extraction of useful information from metabolomics is necessary to structure the pathways. Moreover, the computational algorithms should consider the case that an enzyme connects with at least two substrates at the same time to increase the yield of production. Though the graph-based approach can be used to analyze flux-balanced pathways in the metabolic network (Arabzadeh et al., 2018), it usually needs extra post-processing steps to adjust co-metabolites of the predicted pathway that could be unbalanced. In addition, the prediction of catalytic activities of enzymes has become one of the hot research topics.

An enzyme is a protein catalyst that acts on substrates and converts them into molecules known as products. If a particular function is not assigned to a protein, any reaction catalyzed by that protein will be referred to as a missing enzyme or pathway hole (Green and Karp, 2004). The missing enzymes make it difficult to understand the behaviors of them in the metabolic pathways. The comprehensive and accurate reconstruction of the metabolic pathways in an organism includes the identification of the missing enzymes catalyzing the reactions of the pathways. Basically, identification of missing enzymes contains two steps: selecting candidates and evaluating candidates. The selection of candidates is to find a set of proteins or encoding genes that may catalyze the specific reaction based on some strategies, such as calculating similarities, finding correlations, and so on; and the evaluation of the candidates is to identify the missing enzyme catalyzing the reaction from the candidates to fill in the pathway hole.

Traditional computational efforts to identify missing enzymes in metabolic pathways have focused on finding candidate enzymes based on sequence homology (Green and Karp, 2004). That is, calculating the similarity of a sequence from the organism of interest to sequences that catalyze the same reaction of other organisms with known metabolic pathways. However, such sequence homology methods fail to identify enzymes encoded by genes with poor sequence homology to known metabolic enzymes. To solve the problem, Green and Karp (2004) developed a method that efficiently combined homology and pathway-based evidence to identify candidates; Yamanishi et al. (2007) used supervised network inference to select enzyme encoding gene candidates based on the estimation of the functional association between the genes with respect to chromosomal proximity and evolutionary association; Kharchenko et al. (2006) showed that a number of different types of functional association evidence, including phylogenetic profile co-occurrence, physical clustering of genes on the chromosome and protein interaction data can be used to identify metabolic enzyme encoding genes, and presented two kinds of integration methods, that is, direct likelihood-ratio (DLR) method and alternating decision trees (ADT) built by Adaboost. Since such kind of methods is based on the generally accepted biological hypothesis to build the models, the obtained candidates can more likely fill the pathway hole. However, complicated strategies are usually needed to integrate knowledge into the models.

Now that a huge amount of data from multiple omics, such as transcriptomics, metabonomics, have been accumulated and there are many feature extracting methods (Iqbal et al., 2014; Liu et al., 2015; Du et al., 2017; Liu et al., 2017; Gao and Wu 2018; Wang et al., 2020), some researchers regarded the identification of enzyme candidates as the catalytic and non-catalytic classification problem and built models to classify protein sequences or encoding genes into either catalytic or non-catalytic by using machine learning algorithms such as support vector machine (SVM), K-nearest neighbors (KNN), Bayesian, and RF (Teng et al., 2010; Halperin et al., 2008; Ferrari and Mitchell 2014; Nagao et al., 2014; Amidi et al., 2017). The workflow for classifying protein sequences as catalytic and non-catalytic protein sequences is illustrated in Figure 1. The idea of such kind of methods is very simple. However, large amounts of positive (enzyme) and negative (non-enzyme) should be collected to build the models. Moreover, the predicted results can only answer whether the proteins have catalytic function, but not whether they may catalyze specific reactions.

The purpose of evaluating candidates is to select the missing enzymes catalyzing the specific reactions from the candidates, and there have many approaches been proposed for the evaluation. For example, Green and Karp (2004) proposed Bayesian method to prioritize candidates according to the information on whether the candidate gene is located adjacent to, or in the same transcriptional unit as known enzyme-encoding genes of related metabolic function. Yamanishi et al. (2007) made the prediction of the encoding genes of missing enzymes based on the scores of the candidates and the chemical reaction information encoded in the EC number. The chemical information, including substrates, products, and chemical reactions, can be achieved from their EC numbers, using the KEGG database (Okuda et al., 2008). After the encoding genes are indicated, the functional association between genes concerning evolutionary associations and phylogenetic profiling (Rosetta and Method 2008; Nives and Dessimoz 2015; Zalguizuri et al., 2019) can be estimated and the missing enzyme can be deduced. An example of the phylogenetic profiling for filling the pathway holes is illustrated in Figure 2. Dugé de Bernonville et al. (2020) proposed several prioritization strategies, that is, by homology-based screening, by searching physical gene clusters, by random mutagenesis and by gene co-expression analysis. For the gene clustering or co-expression analysis, some algorithms have been presented to clustering gene sequences into different functional groups (Zhang et al., 2002; Zhong et al., 2005; Bustamam et al., 2017; Sharma and Ali 2017).

The problem of evaluating whether the candidate enzyme catalyzes a specific can also be regarded as the problem of predicting the interaction of substrate-enzyme-product. Chen et al. (2010) developed a KNN model for predicting substrate-enzyme-product triads. In order to measure the nearness between two triads, they defined a novel metric to weigh similarities between substrates, products, and enzymes that were calculated separately. By using their constructed benchmark date set, they got overall accuracy of 95.41%. Niu et al. (2013) also proposed KNN based model combining with mRMR-IFS (Minimum Redundancy Maximum Relevance, Incremental Feature Selection) feature selection method to predict substrate-enzyme-product triads. In order to represent each triad, they encoded substrate/product and enzyme molecules with molecular descriptors and physicochemical properties, respectively, and obtained 290 features; and then they selected 160 features that can be clustered into the ten categories. Testing on the data set that they generated based on KEGG, the model achieved the accuracy of 89.1%. Because these methods directly predict the triads, they can be used not only to predict the missing enzymes catalyzing specific reactions, but also to predict the reactions or metabolites. However, large number of labeled data is needed to promise their good performance.

The metabolites are small molecules which are used in, or created by the chemical reactions occurring in every cell of living organisms. The reactants, intermediates, and products in a metabolic pathway are all called metabolites. Interpreting biochemical characteristics of the metabolites is an essential part of the metabolomics to extend the knowledge of biological systems. It is also the key to the development of many applications in areas such as biotechnology, biomedicine or pharmaceuticals (Nguyen et al., 2019). The identification of the metabolites remains a challenging task in metabolomics with a huge number of potentially interesting but unknown metabolites. Nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry (MS) hyphenated with separation techniques such as liquid chromatography (LC), gas chromatography (GC) and capillary electrophoresis (CE) are the most frequently used techniques to collect large amounts of data on complex biological mixtures or matrices (Wachsmuth et al., 2013). They typically yield complicated spectra or feature-rich chromatograms containing thousands of unknown or unidentified peaks. NMR has the disadvantage that it requires abundant and pure samples, yielding low sensitivity. By contrast, MS is more sensitive and specific, requiring fewer amount of samples (Nguyen et al., 2019). Therefore, most methods for identifying metabolites are based on the MS (Yi et al., 2018). The identification of small molecules from MS data remains a major challenge.

A traditional approach to identifying metabolites is to compare a query MS or MS/MS spectrum of an unknown compound against a database, such as METLIN (Smith et al., 2005), of a number of reference MS or MS/MS spectra. The candidate molecules from the database are ranked based on the similarity of their spectra and the query spectrum and the best matching candidates are returned. Though such methods are reliable, they are only helpful for those unknown metabolites that have reference spectra in the database (Hufsky et al., 2014). Unfortunately, the reference database is often incomplete in reality, leading to unreliable matching results if the reference spectrum of the targeted compound is not contained in the database (Nguyen et al., 2019). To alleviate above problem, a lot of machine learning based approaches have been proposed to predict metabolites via learning the spectra patterns of the known compounds. For example, Kangas et al. (2012) developed an algorithm based on Monte Carlo simulations for identifying metabolites. The algorithm has two phases, illustrated in Figure 3. In the first phase, it predicts bond cleavage energies from which cleavage rates can be calculated based on the ANN (Artificial Neural Network). In the second phase, it generates in silico tandem mass spectra from molecular structures and uses these spectra for the identification. There are roughly two schemas for machine learning methods (Nguyen et al., 2019). Some methods rely on predicting molecular fingerprints from MS/MS data and finding the most similar fingerprint from the molecular structure database (Dührkop et al., 2015; Brouard et al., 2016; Brouard et al., 2019). And the other methods call for predicting MS/MS spectra for a set of candidate molecular structures and choosing the most similar predicted MS/MS spectrum to the observed MS/MS spectrum (Allen et al., 2014; Shen et al., 2014; Djoumbou-Feunang et al., 2019). Those approaches have achieved good identification performance. However, they are highly sensitive and generally cannot model non-linear relationship. It is known that deep learning architecture can be used to build internal representation of large non-linear data, which may lead to superior predictive performance compared to traditional machine learning algorithms. For instance, graph convolution neural network can be directly used to process the graph structure of small molecules, where nodes represent the atoms and edges stand for the bonds between atoms. Moreover, different variants of graph convolution neural network, such as spatial graph convolution networks and spectral graph convolution networks, can be used to optimize the predictive performance.

With the great developments in metabolomics and synthetic biology, on one hand a large amount of data related on metabolic pathways has been generated and been organized in several databases, such as KEGG (Okuda et al., 2008), BioCyc (Karp et al., 2019), and MetaCyc (Karp 2002a; Caspi 2006). On the other hand, it is assumed that a large number of metabolic pathways remain unknown, and many reactions are still missing even in known pathways. What’s more, there is an increasing number of compounds that are known to be present in living organisms but whose synthetic/degradation pathways are unknown. The missing of one or more reactions may result that the pathways from an initial compound to the desired target in an organism are incomplete. Therefore, it is necessary identify such missing reactions during the reconstruction of metabolic pathways. In the field of biosynthesis, finding the potential connection betweeen two known pathways by introducing a novel reaction may lead to a new pathway to the desired product.

Reaction prediction remains a challenging task for investigating metabolic pathways due to resonance structure and specific products that can be redundant and problematic. However, recent machine learning developments have alleviated this problem, resulting in additional performance (Cuperlovic-Culf, 2018). According to whether compounds or pairs of compounds are used in modeling, there are two kinds of roadmaps for reaction prediction: focusing compounds (Kotera et al., 2008; Wei et al., 2016) and focusing compound pairs (Mu et al., 2011; Kotera et al., 2013; Fooshee et al., 2018).

The compound-focused methods identify products or precursors for given compounds and then generate the plausible reactions. For example, Kotera et al. (2008) presented a substructure-based approach to identify possible products and/or precursors for a given compound and to generate a plausible reaction. By using the RF methods, they searched compounds that were structurally related to the target compound, and the structural differences were then checked to determine which of these has the potential to be a product (or precursor) of the target compound in an enzyme-catalyzed reaction. Wei et al. (2016) followed the similar roadmap. Given a set of reagents and reactants, they first built a neural network to predict the reaction type based on a reaction fingerprinting method, and then they used SMARTS (SMiles ARbitrary Target Specification) transformation to predict the likely product from reactants. The neural network workflow starts with reactant and reagent molecules and enumerates all possible electron sources and sinks within the input molecules, based on the atom and bond descriptors, shown in Figure 4. The fingerprinting approach is based on a specific pattern of the molecules, searching occurs all around the molecular structure to detect the presence and absence of the specific pattern in the molecule. The fingerprints for concatenated reactants and reagents become the input for the neural network to predict possible reaction types.

The compound pair-focused methods aim for predicting whether a given compound-compound pair is possibly reactive or not. For instance, Mu et al. (2011) built SVM classifiers to discriminate between functional groups that are reactive and non-reactive. To train the classifiers, they collected positive and negative examples from the KEGG database for each SMARTS-defined substructure, and used atomic properties of atoms in putative reaction centers and molecular properties as features. Kotera et al. (2013) applied a sparsity-induced classifier and SVM to learn whether a compound-compound pair is possibly converted to each other by enzymatic reactions. In order to represent the samples, they defined feature vectors representing the chemical transformation patterns of compound-compound pairs in enzymatic reactions by using chemical fingerprints. Recently, Fooshee et al. (2018) presented a deep learing based reaction prediction method that operated at the level of elementary reactions. Each elementary step involves the movement of electrons from an electron source to an electron sink, and all elementary reactions can be chained together to yield the complex global reaction.