Enhancing Interpretability in Multivariate Metabolomic Modeling through Network-Guided Perturbation-Based Explanations

Enhancing Interpretability in Multivariate Metabolomic Modeling through Network-Guided Perturbation-Based Explanations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhancing Interpretability in Multivariate Metabolomic Modeling through Network-Guided Perturbation-Based Explanations Julia Kuligowski, Abel Albiach, David Pérez-Guaita, Guillermo Quintás This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6742815/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Sep, 2025 Read the published version in Metabolomics → Version 1 posted 10 You are reading this latest preprint version Abstract Multivariate modeling is crucial for uncovering complex patterns in metabolomic data, yet the interpretability of such models remains a major challenge. Here, we propose a network-guided framework that enhances perturbation-based explanations by grouping metabolites according to communities identified in metabolic networks, rather than relying on predefined pathways. Applied to postprandial plasma metabolomic data as a model example, the method revealed both established and novel functional modules relevant to glucose metabolism. The use of metabolite communities derived from network representation in perturbation-based models serves as a complementary tool for the biochemical interpretation of multivariate models, extending beyond fixed, stablished pathways. The strategy is model-agnostic and readily transferable across omics domains, offering a robust tool for improving model interpretability and hypothesis generation in complex biological datasets. metabolomics multivariate analysis perturbation-based explanations interpretability network analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Multivariate modeling of metabolomic data is used for the analysis of complex biochemical systems where researchers prioritize both prediction accuracy and model interpretability. However, it is often the case that models offering less interpretability tend to deliver superior performance. Machine learning methods, which have become the dominant approach for processing multivariate data, often presents challenges in providing interpretable insights into the features driving their predictions. At best, the interpretability of these models remains limited and complex. In response to the increasing need for better model interpretability, a range of methods labeled as explainable artificial intelligence (XAI) or interpretable AI, has emerged[1,2]. These methods explore model behavior by introducing controlled changes or perturbations to the input features and observing the change in the output (e.g., prediction performance in a discriminant model). Thus, a significant change indicates that the altered input features played an important role in the underlying model. This intuitive strategy is broadly applicable across both interpretable methods like Partial Least Squares (PLS), and to black-box models such as Support Vector Machines (SVMs) or artificial neural networks (ANNs). Given the complexity of metabolic processes and the large number of metabolic features measured, In general, perturbation methods typically require clustering metabolites into biologically related groups to facilitate the interpretation of multivariate models. In this sense, metabolism is typically studied by grouping metabolites into pathways. These pathways are designed to represent biochemical reactions connecting substrates and products, providing a framework that categorize metabolites based on the reactions they participate in. The mapping of metabolomic data into these maps or pathways facilitates the interpretation of changes in metabolism as a response to the physiological or experimental changes under study. Previous results combined the use of a perturbation-based strategy for the interpretation of PLS models with the use of metabolic pathways[3–5]. This strategy enabled the rapid identification of biologically meaningful clusters of variables—specifically, metabolites grouped by shared participation in metabolic pathways, and to prioritize the analysis of pathways containing metabolites that contribute most strongly to the model’s predictions. However, this approach presents limitations. The definition of pathways is often arbitrary and varies between sources[6,7]. Moreover, perturbation-based explanations at the pathway level are also limited by difficulties in assessing the impact of both metabolites present in multiple pathways, and the interaction between pathways as subnetworks of a global network[8]. An alternative to clustering metabolic features using predefined pathways is to represent the full metabolic network as a graph composed of all known and predicted reactions in the organism and to group the metabolites based on this network representation[9]. This approach allows for the identification of subnetworks based on their network associations (i.e., as substrates or products of shared metabolic reactions) rather than fixed pathway definitions[10]. Identifying these modules could simplify the analysis of complex, large-scale metabolic networks that hinder conventional pathway-based methods[11]. A key insight from network theory is that many biological systems, including metabolic networks, exhibit community structure reflecting underlying biological functions as densely connected groups (modules) with sparse connections between them. Metabolic networks also share features with other complex systems, such as scale-free topology, small-world properties, and hierarchical modularity[12]. Ravasz et al. proposed that metabolism is organized into small, tightly connected modules that form larger structures in a hierarchical way[13,14]. Recognizing and analyzing this modular structure through network decomposition might provide an alternative functional view of metabolic organization. This study explores the integration of perturbation-based explanation models with a network-driven extension of cluster-based validation frameworks to enhance the interpretability of multivariate metabolomic analyses. By aligning data partitions with the underlying metabolic network organization during perturbation analysis, this alternative clustering enables more robust model interpretation. Data from a previous article that analyzed changes in the metabolome after an oral glucose tolerance test (OGTT) [15] was used in this study as model example. Community structures derived from metabolic network topology were compared to using predefined metabolic pathways. In contrast to pathway-based perturbation methods, where metabolites may belong to multiple pathways, network-based community detection assigns each metabolite to a single community. Overall, this study illustrates for first time how the integration of network topology into perturbation-based explanations offers an alternative approach for improving the interpretability of complex multivariate models in metabolomics. The methodology is model-agnostic, it can be applied to any machine learning algorithm and is readily extensible to other omic domains and regression or classification scenarios. 2. Materials and methods Metabolic network An in-house written MATLAB (MathWorks Inc., Natick, MA, USA) script was used to construct the metabolic network. We first retrieved data from 19437 metabolites from the KEGG database (https://rest.kegg.jp), including identifiers (name, KEGG code), and the list of metabolic pathways and reactions in which they participate. From this dataset, we extracted all substrate–product pairs from the associated reactions to represent directional relationships between metabolites. To focus on biologically relevant compounds, we retained the 1351 metabolites that participate in at least one of the following 35 metabolic pathways: Alanine, aspartate and glutamate metabolism (P1); Amino sugar and nucleotide sugar metabolism (P2); Arginine and proline metabolism (P3); Arginine biosynthesis (P4); Ascorbate and aldarate metabolism (P5); Citrate cycle (TCA cycle) (P6); Cysteine and methionine metabolism (P7); Fructose and mannose metabolism (P8); Glutathione metabolism (P9); Glycerolipid metabolism (P10); Glycerophospholipid metabolism (P11); Glycine, serine and threonine metabolism (P12); Glycolysis / Gluconeogenesis (P13); Histidine metabolism (P14); Linoleic acid metabolism (P15); Lipoic acid metabolism (P16); Lysine degradation (P17); Nicotinate and nicotinamide metabolism (P18); Pentose and glucuronate interconversions (P19); Pentose phosphate pathway (P20); Phenylalanine metabolism (P21); Phenylalanine, tyrosine and tryptophan biosynthesis (P22); Primary bile acid biosynthesis (P23); Purine metabolism (P24); Pyrimidine metabolism (P25); Pyruvate metabolism (P26); Sphingolipid metabolism (P27); Starch and sucrose metabolism (P28); Steroid hormone biosynthesis (P29); Taurine and hypotaurine metabolism (P30); Tryptophan metabolism (P31); Tyrosine metabolism (P32); Valine, leucine and isoleucine biosynthesis (P33); Valine, leucine and isoleucine degradation (P34); and beta-Alanine metabolism (P35). Common high-degree metabolites such as ATP, ADP, AMP, GTP, GDP, UDP, UTP, CTP, dATP, dGTP, dCTP, dTTP, NAD+, NADH, NADP+, NADPH, FAD, FMN, H 2 O, H+, O 2 , CO 2 , NH 3 , H 2 S, Pi (Inorganic phosphate), PPi (Pyrophosphate), sulfate, nitrate, bicarbonate, CoA, 3'',5''-Cyclic AMP, 3'',5''-Cyclic CMP, and adenosine tetraphosphate, were excluded. After this filtering, a total of 1179 metabolites remained for network construction. A directed compound graph was then constructed in Gephi 0.10.1 (released 202301172018) running on Windows 11 (Microsoft), where nodes represent metabolites and edges denote substrate-to-product relationships derived from KEGG reactions. This resulted in a graph with 1179 nodes and 2430 directed edges. The network was visualized using the Force Atlas 2 layout with a scaling factor = 2, and the ‘dissuade hubs’ and ‘prevent overlap’ options enabled. Finally, a set of 15 compounds showed no connections (degree = 0) and were excluded from the network visualization, yielding a final network comprising 1179 nodes and 24309 edges. The excluded compounds were: arachidonate, octanoyl-CoA, dihomo-gamma-linolenate, octanoic acid, 5'-benzoylphosphoadenosine, 9-OxoODE, 9(S)-HODE, 12,13-epoxy-9-hydroxy-10-octadecenoate, 9,12,13-triHOME, 9,10-epoxy-13-hydroxy-11-octadecenoate, 9,10,13-triHOME, 9,10-12,13-diepoxyoctadecanoate, 9,10-dihydroxy-12,13-epoxyoctadecanoate, L-gulose, and L-gulose 1-phosphate. Metabolomic data Experimental metabolomic data were obtained from a previous study investigating time-resolved changes in EDTA plasma metabolites in response to an OGTT. A detailed description of the study design and dataset is available elsewhere[15,16]. The study analyzed samples collected from 15 healthy young male volunteers at baseline and 30 minutes after intake of a 300-mL OGTT solution (Dextro O.G.T., Roche Diagnostics, Mannheim, Germany), containing mono- and oligosaccharides equivalent to 75 g of glucose. Participants were overnight fasted prior to the test. 634 metabolites were analyzed in the samples, combining targeted (132 metabolites using the AbsoluteIDQ p150 kit from Biocrates Life Sciences AG, Innsbruck, Austria) and non-targeted (502 metabolites using the HD4 platform at Metabolon Inc., Durham, USA) platforms. Among them, 159 metabolites included in the metabolic network described above were retained for analysis. When metabolites were measured by both targeted and untargeted analysis, concentrations from the targeted analysis were preferentially used. Partial least squares – Discriminant Analysis (PLS-DA) Partial least squares discriminant analysis (PLS-DA) was used to build multivariate discriminant models to assess differences between the metabolic profiles of samples collected before, and 30 minutes after glucose intake. The data were autoscaled prior to analysis. A double cross-validation (2CV) approach was employed to assess the statistical significance of the between-groups separation[17]. Accordingly, an external test set using a random k-fold split (k = 6 in this study) was selected. The remaining data were further split into internal training and test sets using a leave-one-out cross-validation (LOO-CV, k = N) strategy. This inner loop served to determine the optimal number of latent variables (LVs) for the PLS-DA model applied to the external test set. The process was repeated so that each sample served once as part of the external test set. To ensure robustness, this external-internal CV procedure was iterated 50 times with different random splits. The resulting model descriptors, performance metrics, and predictions obtained over the 50 iterations were averaged to estimate the mean discrimination accuracy, the distribution of predicted values per sample, and to calculate a mean PLS regression vector (b true ). An important advantage of this approach is that the external test samples were never involved in any part of the model training process, including data scaling and LVs selection. This separation enhances the reliability and generalizability of performance estimates. The statistical significance of the 2CV PLS-DA model performance was assessed via permutation testing (250 permutations, significance threshold p < 0.05), as described elsewhere[17]. In each permutation iteration, class labels were randomly shuffled, and the previous 2CV procedure was applied for the assessment of the class separation. The distribution of model performance estimates from these permuted models served as the null distribution to assess the significance of the performance estimate obtained using the real class labels. Additionally, feature selection was performed by comparing the b true vector to the null distribution of 250 b perm vectors obtained from models with permuted class labels. A metabolite was considered statistically significant if its b true value fell outside the 95% confidence interval of its corresponding b perm distribution. PLS-DA was carried out using PLS Toolbox 9.5 (Eigenvector Research Inc., Wenatchee, WA, USA) and custom scripts written in MATLAB 2021a (MathWorks Inc., Natick, MA, USA). Perturbation-based Explanations Perturbation-based explanations were conducted as an adaptation of a previously established method known as cluster-CV[3]. Cluster-CV is a perturbation-based approach designed to evaluate the impact of groups of features on the predictive performance of a PLS model. In this study, feature grouping for perturbation-based explanations was defined at two levels: i) at the pathway level, using sets of features included in the 35 previously listed metabolic pathways, and ii) using communities identified by modularity analysis of the metabolic network using Louvain algorithm[18].Thus, while a metabolite can be included in several pathways, it can only be included in a single network community. During the perturbation test, the value of those features included in each subset (e.g., metabolites in a metabolic pathway or network community) were permuted feature-wise. Then, a PLS-DA of the modified dataset was built, and its mean predictive performance (e.g., classification accuracy) was estimated through repeated (n=10) random 6-fold CV. This process was repeated 50 times to average the effect of random permutations on the results. The distribution of performance estimates obtained from the model built using perturbed data was compared to those from the original model. A decrease in predictive performance after permuting a metabolic subset indicated that these metabolites collectively contributed significantly to the initial model. Scripts and the Gephi Network file used in the study are available in Zenodo (DOI: 10.5281/zenodo.15387946). 3. Results and discussion Metabolic network analysis We constructed a directed network comprising 1164 nodes and 2438 edges, representing metabolites and reactions involving metabolites as products or substrates, respectively. The network exhibited a low density (0.002), consistent with a sparsely connected topology. The average node degree was 2.09. The average shortest path length was 3.14, and the network diameter was 12, indicating the presence of relatively long-range interactions among certain nodes. To explore community structure, we applied the Louvain algorithm (resolution = 1.0; randomized; weighted), which yielded a modularity score of 0.72—indicative of a well-defined modular organization. The network contained 6 weakly connected components, although most nodes were part of the largest connected component. Figure 1 (left panel) shows the constructed network, with the 24 distinct communities represented as different colours, with community sizes ranging from 2 to 128 metabolites. To better understand the functional composition of each community, we visualized the distribution of biological pathways within each modularity class ( Figure 2 ). Each plot indicates the number of metabolites included in a metabolic pathway within each community, labeled consistently across all communities. Several communities exhibited strong enrichment for specific pathways, suggesting functional compartmentalization within the network. For instance, communities 18-19 and 21-24 included metabolites sharing a unique metabolic pathway, suggesting functional specialization. While some of these pathway-specific communities contained few metabolites, others included more complex pathways— such as community 22, involved in Linoleic acid metabolism (P15, nodes = 16)) and community 24, related to Nicotinate and nicotinamide metabolism (P18, nodes = 30)). On the other hand, others displayed a more diverse composition (e.g., Communities 1, 2, 4, or 5). Although metabolites can be included in several pathways simultaneously, this suggests both pathway-specific and cross-pathway modular organization within the metabolic network. Figure 3 shows the community composition for each metabolic pathway where each pie chart represents a single pathway and illustrates the distribution of metabolites across modularity-defined communities. While some pathways were broadly represented (e.g., Amino sugar and nucleotide metabolism, Glycine, serine and threonine metabolism, or Cysteine and methionine metabolism), others appeared in only a single or in a small number of communities (e.g., Steroid hormone biosynthesis, Starch and sucrose metabolism, or Arginine biosynthesis). These distribution patterns reflect whether a pathway was primarily localized within a single module or dispersed across several, potentially indicating its role as a hub. The limited overlap between metabolic pathways and modularity-defined communities was expected, as pathway databases often do not capture the topological organization of metabolic networks. On the other hand, modularity-based communities reflect patterns of network connectivity and are not constrained by predefined biological functions and so, they can potentially uncover functional modules not readily apparent in pathway maps, where metabolites present in multiple communities may function as intermediate nodes, facilitating cross-talk between metabolic functions. So, these communities could be valuable in the context of multivariate models and perturbation-based analyses, where feature grouping may enhance interpretability. Postprandial changes in the plasma metabolome after glucose intake The metabolites included in the OGTT data set were mapped onto the metabolic graph depicted in Figure 1 (middle). Among the 634 metabolites included in the OGTT study, only a fraction (25%) overlapped with the full network. Partial coverage (159 metabolites, 14% of the nodes of the network, see green nodes in Figure 1 ) is frequently observed in metabolomics studies, due to both limitations in metabolic coverage and network information. The OGTT subset showed uneven representation across communities (see Figure 4, top ) and annotated KEGG pathways (see Figure 4, bottom ), highlighting regions of both strong and limited coverage. Despite this, the subset encompassed functionally relevant modules and pathways, supporting its utility for downstream network-based analyses. First, we performed univariate based analysis of each metabolite. A total of 15 metabolites (9.5% of the 159 included in the whole network) showed a significant increase (glucose, fructose, maltose, lactate, glycocholate, glycochenodeoxycholate, and creatine) or decrease (cortisone, ethanolamine phosphate, glycerol, citrulline, xanthine, spermidine, cortisol, and guanidinoacetate) in their postprandial concentrations following glucose intake (t-test p-value<0.05). To identify metabolic pathways significantly altered after glucose intake, pathway analysis was performed using autoscaled data. The global test was selected as the enrichment method, with relative betweenness centrality used as the topology measure, based on the KEGG Homo sapiens library. As shown in Figure 5 , the most significantly affected pathway was ‘starch and sucrose metabolism’ (FDR = 0.003, impact = 0.50). Additionally, with very low impacts, ‘galactose metabolism’ (FDR = 0.003, impact = 0.03) and ‘steroid hormone biosynthesis’ (FDR = 0.02, impact = 0.04) were found altered. To further evaluate metabolic differences between pre- and post-glucose intake using multivariate analysis, supervised PLS-DA was employed. A 2CV strategy was used for the assessment of the statistical significance of the difference between classes, as described previously. The classification results from the 2CV of PLS-DA are shown in Figure 6 , achieving a cross-validated accuracy of 79%. Statistical significance of the observed separation was evaluated via permutation testing (n = 250), confirming discrimination with p-value < 0.005. Furthermore, regression vectors obtained during the permutation test were used as null distribution to identify 44 metabolites with statistically significant (p-value < 0.05) values in the regression vector of the PLS model built using the true class labels. Figure 6 displays the PLS regression vector and the Variable Importance in Projection (VIP) scores, highlighting the set of 44 metabolites contributing significantly to the class separation. Results from enrichment analysis on this subset using KEGG human metabolic pathways as metabolite set library, indicated as significantly altered the ‘Arginine and proline metabolism’, ‘Arginine biosynthesis’, and ‘Nicotinate and nicotinamide metabolism’ pathways. Overall, the univariate analysis identified metabolites exhibiting large individual changes in concentration post-OGTT, highlight selective pathway-level changes particularly in carbohydrate metabolism. In contrast, the multivariate PLS-DA approach, validated by CV and permutation testing, showed broader metabolic effects involving also amino acid metabolism and nicotinate and nicotinamide pathways. Despite these differences, there was a significant overlap between the approaches, as the set of 44 metabolites selected by PLS-DA included the 15 identified as significant by univariate analysis. This divergence between univariate and multivariate findings is consistent with the different statistical sensitivities of the methods: univariate tests are optimized to detect individual effects, whereas multivariate models capture patterns of covariation across multiple metabolites that may not be individually significant[19]. Perturbation-Based Explanations To enhance interpretability of metabolic changes underlying the PLS-DA discrimination of samples collected before and after glucose intake, we applied a perturbation-based approach assessing model sensitivity to systematic feature alteration. In this study, feature clustering for perturbation-based explanations was defined at two levels: i) at the pathway level and ii) using communities identified by modularity analysis of a metabolic network. Perturbation-based explanations at the pathway level used sets of features defined in the 35 previously listed metabolic pathways. The second approach classified detected metabolites in the study according to the assigned community from modularity analysis of the metabolic network. Figure 7 shows the distributions of classification accuracies obtained using both methods, where lower predictive performance after permuting than in the model built using true class labels (red dotted line in the figure), indicates that these metabolites collectively contributed significantly to the initial model. Pathway-based perturbation analysis indicated the significance of metabolites included in the ‘Steroid hormone biosynthesis’ (7), and with lower significance, ‘Starch and sucrose metabolism’ (3), ‘beta-alanine metabolism’ (8), and ‘Fructose and mannose metabolism’ (4) (the number within parenthesis indicate the number of metabolites of these pathways present in the data set), with a single metabolite (D-Fructose) present in more than one of these pathways (see upset plot in Figure 8 ). On the other hand, using a perturbation analysis based on modularity-defined communities found two communities whose permutation led to significantly lower predictive performance than in the original model: Communities 13 (10 metabolites), 8 (5 metabolites), and 4 (14 metabolites) (see Figure 7 ). As shown in Figure 9 , community 13 included mainly metabolites participating in the ‘Steroid hormone biosynthesis’ pathway (cholesterol, D-glucuronate, cortisol, cortisone, dehydroepiandrosterone sulfate, urocortisol, cortolone, and etiocholan-3α-ol-17-one 3-glucuronide) and in the ‘Primary bile acid biosynthesis’ (cholesterol, 3β,7α-dihydroxy-5-cholestenoate, and 7α-hydroxy-3-oxo-4-cholestenoate). Community 8 included metabolites involved in ‘Starch and sucrose metabolism’ (glucose, fructose, and maltose), ‘Fructose and mannose metabolism’ (fructose, maltose, mannitol), and ‘Aminosugar and nucleotide sugar metabolism’ (glucose, fructose, and maltose), as well as ‘Gluconeogenesis’ (glucose) and ‘Pentose phosphate pathway’ (glucose). Community 4 showed a more diverse composition including pyruvate and other metabolites participating in several pathways simultaneously such as ‘Cysteine and methionine metabolism’, ‘Alanine, aspartate and glutamate metabolism’, ‘Glycine, serine and threonine metabolism’, ‘Tryptophan metabolism’ (serotonin, indole-3-acetate, 5-hydroxyindolacetate), as well as ‘Fructose and mannose metabolism’, and ‘Gluconeogenesis’ (lactate), among others. While pathway-based perturbation analysis identified well-established metabolic pathways, such as ‘ Steroi d hormone biosynthesis’, as important contributors to model performance, its interpretability was limited by overlapping metabolites across pathways. In contrast, the network-based approach grouped metabolites into non-overlapping communities based on metabolic network structure, allowing a more straightforward attribution of predictive relevance. Some communities aligned with known pathways, while others spanned multiple pathways, offering complementary insights into metabolic clusters contributing to model performance. For example, community 13 captured similar biology to the pathway analysis, reinforcing their relevance, while others such as Community 4 represented metabolite groups spanning multiple pathways. 4. Conclusions In this study, we propose a network-guided framework for enhancing the interpretability of multivariate metabolomic models through perturbation-based explanations. By using community structures derived from metabolic network topology rather than predefined metabolic pathways, metabolite grouping can be simplified, overcoming redundancy and offering a complementary biological perspective. Application to postprandial metabolic data identified both known and potentially novel functional modules, showing the usefulness of this approach to identify patterns beyond known pathway annotations. However, the approach presents limitations. A partial metabolomic coverage relative to the complete metabolic network may restrict the generalizability of the findings. Besides, further refinement of network construction and community detection methods may also enhance the biological relevance of detected modules. Overall, this study illustrates that integrating network topology into perturbation-based explanations offers a straightforward direction for improving the interpretability of complex multivariate models in metabolomics. Declarations Acknowledgements GQ acknowledges the grant PID2021-125573OB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF A way of making Europe, EU. This work was supported by the Carlos III Health Institute, Ministry of Economy and Competitiveness, Spain [grant numbers CPII21/00003, PI20/00964, and PI23/00202] co-funded by European Regional Development Fund “A way to make Europe”) and MCIN/AEI/10.13039/501100011033 and, as appropriate, by “European Union NextGenerationEU/PRTR” [grant number CNS2022-135398]. Authors acknowledge the financial support of projects PID2023-148947OB-I00, RYC2019-026556-I, CNS2023-145528 funded by MCIN/AEI/10.13039/501100011033. References M. Ivanovs, R. Kadikis, K. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6742815","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":463842002,"identity":"650c0459-5542-4602-aec3-3b1ef8598056","order_by":0,"name":"Julia Kuligowski","email":"","orcid":"","institution":"Health Research Institute Hospital La Fe","correspondingAuthor":false,"prefix":"","firstName":"Julia","middleName":"","lastName":"Kuligowski","suffix":""},{"id":463842003,"identity":"46464c9c-bb6b-4d52-83e8-37c512f114c8","order_by":1,"name":"Abel Albiach","email":"","orcid":"","institution":"Health Research Institute Hospital La Fe","correspondingAuthor":false,"prefix":"","firstName":"Abel","middleName":"","lastName":"Albiach","suffix":""},{"id":463842004,"identity":"566396bb-8f8c-4954-a279-938321ac5fcd","order_by":2,"name":"David Pérez-Guaita","email":"","orcid":"","institution":"University of Valencia","correspondingAuthor":false,"prefix":"","firstName":"David","middleName":"","lastName":"Pérez-Guaita","suffix":""},{"id":463842005,"identity":"73cea2ff-80f4-4882-a29b-b1a2ae2a3f4a","order_by":3,"name":"Guillermo Quintás","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYJCCAyCCnx3KIFJLAgODZDOQcYDBgFhNQC0Gh8GaidAi755jeLjwh5298WHmg4c/1Pxh4Jc+fgGvFsMzbwwOz0hITtx2mC3hwIFjBgySfTkF+LXMyDE4zJPAnGB2mMfgwAE2AwaDMzwJxGiptzdu5v9w4MA/IrTIS4C1HGbcwMzDcOBgG0gL+wG8Wgx4nhUc5kk7njjjMJvBgbN9xjySPTx4dTDItydv/sxjU23P3978+EPFNzk5fh72B/htOYDmcKAVPPgjR74hAUOMgC2jYBSMglEw4gAAR9JJQO0YiIEAAAAASUVORK5CYII=","orcid":"","institution":"Leitat Technological Center","correspondingAuthor":true,"prefix":"","firstName":"Guillermo","middleName":"","lastName":"Quintás","suffix":""}],"badges":[],"createdAt":"2025-05-25 09:09:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6742815/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6742815/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11306-025-02347-8","type":"published","date":"2025-09-26T15:57:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83681010,"identity":"7424ddb5-4d56-4add-9449-5c453b6ab011","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":175984,"visible":true,"origin":"","legend":"\u003cp\u003eCommunity structure of the metabolic network. Nodes represent individual metabolites, and edges denote directed associations through a chemical reaction. Left) Colors indicate modularity-based community assignments, revealing clusters of metabolites with higher internal connectivity. Labeled key nodes such as SAM, SAHC, or Pyruvate reflect highly connected or biochemically central metabolites. This modular organization suggests potential functional groupings and metabolic sub-networks, some of which may serve as hubs for integration or regulatory control. Center) Distribution of metabolites included in the OGTT data set (green nodes) and not included in the OGTT data set (pink nodes). Right) Network showing as color scale the classification accuracy estimated from the network-guided perturbation test (darker red color indicate lower levels of classification accuracy in the test). All metabolites of the community included in the perturbation test were colored regardless of their presence in the OGTT data set.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/cddfdb11531dd6ab2133cf86.png"},{"id":83681017,"identity":"9453328d-1722-41b4-add8-5e7f0b22e205","added_by":"auto","created_at":"2025-05-30 16:08:45","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":142360,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eDistribution of metabolites across network communities and associated pathway composition.\u003c/em\u003e\u003cbr\u003e\nBarplots represent the pathway composition of each community. Each bar corresponds to a globally assigned pathway code (e.g., P1, P2). Note: a single metabolite can be included in several pathways. Metabolic pathways: Alanine, aspartate and glutamate metabolism (P1); Amino sugar and nucleotide sugar metabolism (P2); Arginine and proline metabolism (P3); Arginine biosynthesis (P4); Ascorbate and aldarate metabolism (P5); Citrate cycle (TCA cycle) (P6); Cysteine and methionine metabolism (P7); Fructose and mannose metabolism (P8); Glutathione metabolism (P9); Glycerolipid metabolism (P10); Glycerophospholipid metabolism (P11); Glycine, serine and threonine metabolism (P12); Glycolysis / Gluconeogenesis (P13); Histidine metabolism (P14); Linoleic acid metabolism (P15); Lipoic acid metabolism (P16); Lysine degradation (P17); Nicotinate and nicotinamide metabolism (P18); Pentose and glucuronate interconversions (P19); Pentose phosphate pathway (P20); Phenylalanine metabolism (P21); Phenylalanine, tyrosine and tryptophan biosynthesis (P22); Primary bile acid biosynthesis (P23); Purine metabolism (P24); Pyrimidine metabolism (P25); Pyruvate metabolism (P26); Sphingolipid metabolism (P27); Starch and sucrose metabolism (P28); Steroid hormone biosynthesis (P29); Taurine and hypotaurine metabolism (P30); Tryptophan metabolism (P31); Tyrosine metabolism (P32); Valine, leucine and isoleucine biosynthesis (P33); Valine, leucine and isoleucine degradation (P34); and beta-Alanine metabolism (P35).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/3e1eec3a5de61732cb031c62.png"},{"id":83681014,"identity":"8138fa8e-a876-4ba8-9ee4-d43a11637da1","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":165165,"visible":true,"origin":"","legend":"\u003cp\u003eCommunity composition for selected metabolic pathways. Each pie chart represents a single pathway and illustrates the distribution of metabolites across modularity-defined communities.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/9b3998be29463446dd9b0571.png"},{"id":83681016,"identity":"92373530-399a-438f-8bdb-abef473c2681","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":147163,"visible":true,"origin":"","legend":"\u003cp\u003eTop) Number of metabolites included in each community, and in the OGTT data subset; Bottom) Number of metabolites included in each metabolic pathway in the network and in the OGTT data subset (Note: a metabolite can be included in several pathways).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/cc1ec82448a890c6910287ae.png"},{"id":83681008,"identity":"97fc281d-20b2-4026-a8ee-b8ce402d8974","added_by":"auto","created_at":"2025-05-30 16:08:42","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":18926,"visible":true,"origin":"","legend":"\u003cp\u003eResults from pathway analysis of the OGTT data subset.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/4f7d2631e1c0a4e61e7b53ad.png"},{"id":83681012,"identity":"c655c5b2-70d7-4d76-ba3a-adf956707a1a","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":134484,"visible":true,"origin":"","legend":"\u003cp\u003eLeft) Predicted values by 2CV of PLS−DA for the discrimination between samples collected before and 30 min after glucose intake; Right) PLS regression vector of a model using 5 latent variables and the associated Variable Importance in Projection (VIP) scores, highlighting the metabolites found statistically significant in the discrimination, based on results from a permutation test (p-value\u0026lt;0.05).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/0956defad1011154ca39f6dd.png"},{"id":83681011,"identity":"295f9441-c073-42a7-a852-0a5b977abc9e","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":200685,"visible":true,"origin":"","legend":"\u003cp\u003eResults from perturbation-Based Explanations conducted to evaluate the impact of clusters of features on the predictive performance of a PLS model. Feature clustering for perturbation-based explanations was defined at the pathway level (left) and using communities identified by modularity analysis of a metabolic network (right).\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/111e84b340e530883dcdb34c.png"},{"id":83681013,"identity":"538bffbb-32ee-4846-a1f3-ec09b4abeb39","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":27669,"visible":true,"origin":"","legend":"\u003cp\u003eUpset plot of the overlap among metabolites present in the OGTT data subset in three metabolic pathways (Steroid hormone biosynthesis, Starch and fructose metabolism, and Fructose and mannose metabolism).\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/090809c59e28a7c59de452f9.png"},{"id":83681015,"identity":"b6013a41-59ba-4a1e-8d4a-273dbe7118a8","added_by":"auto","created_at":"2025-05-30 16:08:44","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":196455,"visible":true,"origin":"","legend":"\u003cp\u003eBar plots)\u003cstrong\u003e \u003c/strong\u003eDistribution of metabolites included in six selected network communities across different metabolic pathways in the whole network (grey bar) and in the OGTT data subset (blue bar). Center plot) Localization of the metabolites included in communities 13, 8, 4, and 12.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/ab22fcd755cc121301955887.png"},{"id":92430421,"identity":"5bea11ef-1775-49f7-af05-fe4b578ed2e8","added_by":"auto","created_at":"2025-09-29 16:02:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1499686,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6742815/v1/82c3f80d-10de-4a61-8a39-a4cba0c64211.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhancing Interpretability in Multivariate Metabolomic Modeling through Network-Guided Perturbation-Based Explanations","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMultivariate modeling of metabolomic data is used for the analysis of complex biochemical systems where researchers prioritize both prediction accuracy and model interpretability. However, it is often the case that models offering less interpretability tend to deliver superior performance. Machine learning methods, which have become the dominant approach for processing multivariate data, often presents challenges in providing interpretable insights into the features driving their predictions. At best, the interpretability of these models remains limited and complex. In response to the increasing need for better model interpretability, a range of methods labeled as explainable artificial intelligence (XAI) or interpretable AI, has emerged[1,2]. These methods explore model behavior by introducing controlled changes or perturbations to the input features and observing the change in the output (e.g., prediction performance in a discriminant model). Thus, a significant change indicates that the altered input features played an important role in the underlying model. This intuitive strategy is broadly applicable across both interpretable methods like Partial Least Squares (PLS), and to black-box models such as Support Vector Machines (SVMs) or artificial neural networks (ANNs).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eGiven the complexity of metabolic processes and the large number of metabolic features measured, In general, perturbation methods typically require clustering metabolites into biologically related groups to facilitate the interpretation of multivariate models. In this sense, metabolism is typically studied by grouping metabolites into pathways. These pathways are designed to represent biochemical reactions connecting substrates and products, providing a framework that categorize metabolites based on the reactions they participate in. The mapping of metabolomic data into these maps or pathways facilitates the interpretation of changes in metabolism as a response to the physiological or experimental changes under study. Previous results combined the use of a perturbation-based strategy for the interpretation of PLS models with the use of metabolic pathways[3\u0026ndash;5]. This strategy enabled the rapid identification of biologically meaningful clusters of variables\u0026mdash;specifically, metabolites grouped by shared participation in metabolic pathways, and to prioritize the analysis of pathways containing metabolites that contribute most strongly to the model\u0026rsquo;s predictions. However, this approach presents limitations.\u0026nbsp;The definition of pathways is often arbitrary and varies between sources[6,7]. Moreover, perturbation-based explanations at the pathway level are also limited by difficulties in assessing the impact of both metabolites present in multiple pathways, and the interaction between pathways as subnetworks of a global network[8]. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAn alternative to clustering metabolic features using predefined pathways is to represent the full metabolic network as a graph composed of all known and predicted reactions in the organism and to group the metabolites based on this network representation[9]. This approach allows for the identification of subnetworks based on their network associations (i.e., as substrates or products of shared metabolic reactions) rather than fixed pathway definitions[10]. Identifying these modules could simplify the analysis of complex, large-scale metabolic networks that hinder conventional pathway-based methods[11]. A key insight from network theory is that many biological systems, including metabolic networks, exhibit \u003cem\u003ecommunity structure\u0026nbsp;\u003c/em\u003ereflecting underlying biological functions as densely connected groups (modules) with sparse connections between them. Metabolic networks also share features with other complex systems, such as scale-free topology, small-world properties, and hierarchical modularity[12]. Ravasz et al. proposed that metabolism is organized into small, tightly connected modules that form larger structures in a hierarchical way[13,14]. Recognizing and analyzing this modular structure through network decomposition might provide an alternative functional view of metabolic organization.\u003c/p\u003e\n\u003cp\u003eThis study explores the integration of perturbation-based explanation models with a network-driven extension of cluster-based validation frameworks to enhance the interpretability of multivariate metabolomic analyses. By aligning data partitions with the underlying metabolic network organization during perturbation analysis, this alternative clustering enables more robust model interpretation. Data from a previous article that analyzed changes in the metabolome after an oral glucose tolerance test (OGTT) [15] \u0026nbsp;was used in this study as model example. Community structures derived from metabolic network topology were compared to using predefined metabolic pathways. In contrast to pathway-based perturbation methods, where metabolites may belong to multiple pathways, network-based community detection assigns each metabolite to a single community. Overall, this study illustrates for first time how the integration of network topology into perturbation-based explanations offers an alternative approach for improving the interpretability of complex multivariate models in metabolomics. The methodology is model-agnostic, it can be applied to any machine learning algorithm and is readily extensible to other omic domains and regression or classification scenarios.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cp\u003e\u003cstrong\u003eMetabolic network\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAn in-house written MATLAB (MathWorks Inc., Natick, MA, USA) script was used to construct the metabolic network. \u0026nbsp;We first retrieved data from 19437 metabolites from the KEGG database (https://rest.kegg.jp), including identifiers (name, KEGG code), and the list of metabolic pathways and reactions in which they participate. From this dataset, we extracted all substrate–product pairs from the associated reactions to represent directional relationships between metabolites. To focus on biologically relevant compounds, we retained the 1351 metabolites that participate in at least one of the following 35 metabolic pathways: Alanine, aspartate and glutamate metabolism (P1); Amino sugar and nucleotide sugar metabolism (P2); Arginine and proline metabolism (P3); Arginine biosynthesis (P4); Ascorbate and aldarate metabolism (P5); Citrate cycle (TCA cycle) (P6); Cysteine and methionine metabolism (P7); Fructose and mannose metabolism (P8); Glutathione metabolism (P9); Glycerolipid metabolism (P10); Glycerophospholipid metabolism (P11); Glycine, serine and threonine metabolism (P12); Glycolysis / Gluconeogenesis (P13); Histidine metabolism (P14); Linoleic acid metabolism (P15); Lipoic acid metabolism (P16); Lysine degradation (P17); Nicotinate and nicotinamide metabolism (P18); Pentose and glucuronate interconversions (P19); Pentose phosphate pathway (P20); Phenylalanine metabolism (P21); Phenylalanine, tyrosine and tryptophan biosynthesis (P22); Primary bile acid biosynthesis (P23); Purine metabolism (P24); Pyrimidine metabolism (P25); Pyruvate metabolism (P26); Sphingolipid metabolism (P27); Starch and sucrose metabolism (P28); Steroid hormone biosynthesis (P29); Taurine and hypotaurine metabolism (P30); Tryptophan metabolism (P31); Tyrosine metabolism (P32); Valine, leucine and isoleucine biosynthesis (P33); Valine, leucine and isoleucine degradation (P34); and beta-Alanine metabolism (P35). Common high-degree metabolites such as ATP, ADP, AMP, GTP, GDP, UDP, UTP, CTP, dATP, dGTP, dCTP, dTTP, NAD+, NADH, NADP+, NADPH, FAD, FMN, H\u003csub\u003e2\u003c/sub\u003eO, H+, O\u003csub\u003e2\u003c/sub\u003e, CO\u003csub\u003e2\u003c/sub\u003e, NH\u003csub\u003e3\u003c/sub\u003e, H\u003csub\u003e2\u003c/sub\u003eS, Pi (Inorganic phosphate), PPi (Pyrophosphate), sulfate, nitrate, bicarbonate, CoA, 3'',5''-Cyclic AMP, 3'',5''-Cyclic CMP, and adenosine tetraphosphate, were excluded. After this filtering, a total of 1179 metabolites remained for network construction.\u003c/p\u003e\n\u003cp\u003eA directed compound graph was then constructed in Gephi 0.10.1 (released 202301172018) running on Windows 11 (Microsoft), where nodes represent metabolites and edges denote substrate-to-product relationships derived from KEGG reactions. This resulted in a graph with 1179 nodes and 2430 directed edges. The network was visualized using the Force Atlas 2 layout with a scaling factor = 2, and the ‘dissuade hubs’ and ‘prevent overlap’ options enabled. \u0026nbsp;Finally, a set of 15 compounds showed no connections (degree = 0) and were excluded from the network visualization, yielding a final network comprising 1179 nodes and 24309 edges. The excluded compounds were: arachidonate, octanoyl-CoA, dihomo-gamma-linolenate, octanoic acid, 5'-benzoylphosphoadenosine, 9-OxoODE, 9(S)-HODE, 12,13-epoxy-9-hydroxy-10-octadecenoate, 9,12,13-triHOME, 9,10-epoxy-13-hydroxy-11-octadecenoate, 9,10,13-triHOME, 9,10-12,13-diepoxyoctadecanoate, 9,10-dihydroxy-12,13-epoxyoctadecanoate, L-gulose, and L-gulose 1-phosphate.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMetabolomic data\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eExperimental metabolomic data were obtained from a previous study investigating time-resolved changes in EDTA plasma metabolites in response to an OGTT. A detailed description of the study design and dataset is available elsewhere[15,16]. The study analyzed samples collected from 15 healthy young male volunteers at baseline and 30 minutes after intake of a 300-mL OGTT solution (Dextro O.G.T., Roche Diagnostics, Mannheim, Germany), containing mono- and oligosaccharides equivalent to 75 g of glucose. Participants were overnight fasted prior to the test. 634 metabolites were analyzed in the samples, combining targeted (132 metabolites using the AbsoluteIDQ p150 kit from Biocrates Life Sciences AG, Innsbruck, Austria) and non-targeted (502 metabolites using the HD4 platform at Metabolon Inc., Durham, USA) platforms. Among them, 159 metabolites included in the metabolic network described above were retained for analysis. When metabolites were measured by both targeted and untargeted analysis, concentrations from the targeted analysis were preferentially used.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePartial least squares – Discriminant Analysis (PLS-DA)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePartial least squares discriminant analysis (PLS-DA) was used to build multivariate discriminant models to assess differences between the metabolic profiles of samples collected before, and 30 minutes after glucose intake. The data were autoscaled prior to analysis. A double cross-validation (2CV) approach was employed to assess the statistical significance of the between-groups separation[17]. Accordingly, an external test set using a random k-fold split (k = 6 in this study) was selected. The remaining data were further split into internal training and test sets using a leave-one-out cross-validation (LOO-CV, k = N) strategy. This inner loop served to determine the optimal number of latent variables (LVs) for the PLS-DA model applied to the external test set. The process was repeated so that each sample served once as part of the external test set. To ensure robustness, this external-internal CV procedure was iterated 50 times with different random splits. The resulting model descriptors, performance metrics, and predictions obtained over the 50 iterations were averaged to estimate the mean discrimination accuracy, the distribution of predicted values per sample, and to calculate a mean PLS regression vector (b\u003csub\u003etrue\u003c/sub\u003e). An important advantage of this approach is that the external test samples were never involved in any part of the model training process, including data scaling and LVs selection. This separation enhances the reliability and generalizability of performance estimates. The statistical significance of the 2CV PLS-DA model performance was assessed via permutation testing (250 permutations, significance threshold p \u0026lt; 0.05), as described elsewhere[17]. In each permutation iteration, class labels were randomly shuffled, and the previous 2CV procedure was applied for the assessment of the class separation. The distribution of model performance estimates from these permuted models served as the null distribution to assess the significance of the performance estimate obtained using the real class labels.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAdditionally, feature selection was performed by comparing the b\u003csub\u003etrue\u003c/sub\u003e vector to the null distribution of 250 b\u003csub\u003eperm\u003c/sub\u003e vectors obtained from models with permuted class labels. A metabolite was considered statistically significant if its b\u003csub\u003etrue\u003c/sub\u003e value fell outside the 95% confidence interval of its corresponding b\u003csub\u003eperm\u003c/sub\u003e distribution.\u003c/p\u003e\n\u003cp\u003ePLS-DA was carried out using PLS Toolbox 9.5 (Eigenvector Research Inc., Wenatchee, WA, USA) and custom scripts written in MATLAB 2021a (MathWorks Inc., Natick, MA, USA).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePerturbation-based Explanations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePerturbation-based explanations were conducted as an adaptation of a previously established method known as cluster-CV[3]. Cluster-CV is a perturbation-based approach designed to evaluate the impact of groups of features on the predictive performance of a PLS model. In this study, feature grouping for perturbation-based explanations was defined at two levels: i) at the pathway level, using sets of features included in the 35 previously listed metabolic pathways, and ii) using communities identified by modularity analysis of the metabolic network using Louvain algorithm[18].Thus, while a metabolite can be included in several pathways, it can only be included in a single network community.\u003c/p\u003e\n\u003cp\u003eDuring the perturbation test, the value of those features included in each subset (e.g., metabolites in a metabolic pathway or network community) were permuted feature-wise. Then, a PLS-DA of the modified dataset was built, and its mean predictive performance (e.g., classification accuracy) was estimated through repeated (n=10) random 6-fold CV. This process was repeated 50 times to average the effect of random permutations on the results. The distribution of performance estimates obtained from the model built using perturbed data was compared to those from the original model. A decrease in predictive performance after permuting a metabolic subset indicated that these metabolites collectively contributed significantly to the initial model.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eScripts and the Gephi Network file used in the study are available in Zenodo (DOI: 10.5281/zenodo.15387946).\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eMetabolic network analysis\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe constructed a directed network comprising 1164 nodes and 2438 edges, representing metabolites and reactions involving metabolites as products or substrates, respectively. The network exhibited a low density (0.002), consistent with a sparsely connected topology. The average node degree was 2.09. The average shortest path length was 3.14, and the network diameter was 12, indicating the presence of relatively long-range interactions among certain nodes. To explore community structure, we applied the Louvain algorithm (resolution = 1.0; randomized; weighted), which yielded a modularity score of 0.72\u0026mdash;indicative of a well-defined modular organization. The network contained 6 weakly connected components, although most nodes were part of the largest connected component. \u003cstrong\u003eFigure 1\u003c/strong\u003e (left panel) shows the constructed network, with the 24 distinct communities represented as different colours, with community sizes ranging from 2 to 128 metabolites. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo better understand the functional composition of each community, we visualized the distribution of biological pathways within each modularity class (\u003cstrong\u003eFigure 2\u003c/strong\u003e). Each plot indicates the number of metabolites included in a metabolic pathway within each community, labeled consistently across all communities. Several communities exhibited strong enrichment for specific pathways, suggesting functional compartmentalization within the network. For instance, communities 18-19 and 21-24 included metabolites sharing a unique metabolic pathway, suggesting functional specialization. While some of these pathway-specific communities contained few metabolites, others included more complex pathways\u0026mdash; such as community 22, involved in Linoleic acid metabolism (P15, nodes = 16)) and community 24, related to Nicotinate and nicotinamide metabolism (P18, nodes = 30)). On the other hand, others displayed a more diverse composition (e.g., Communities 1, 2, 4, or 5). Although metabolites can be included in several pathways simultaneously, this suggests both pathway-specific and cross-pathway modular organization within the metabolic network.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFigure 3\u003c/strong\u003e shows the community composition for each metabolic pathway where each pie chart represents a single pathway and illustrates the distribution of metabolites across modularity-defined communities. While some pathways were broadly represented (e.g., Amino sugar and nucleotide metabolism, Glycine, serine and threonine metabolism, or Cysteine and methionine metabolism), others appeared in only a single or in a small number of communities (e.g., Steroid hormone biosynthesis, Starch and sucrose metabolism, or Arginine biosynthesis). These distribution patterns reflect whether a pathway was primarily localized within a single module or dispersed across several, potentially indicating its role as a hub. The limited overlap between metabolic pathways and modularity-defined communities was expected, as pathway databases often do not capture the topological organization of metabolic networks. On the other hand, modularity-based communities reflect patterns of network connectivity and are not constrained by predefined biological functions and so, they can potentially uncover functional modules not readily apparent in pathway maps, where metabolites present in multiple communities may function as intermediate nodes, facilitating cross-talk between metabolic functions. So, these communities could be valuable in the context of multivariate models and perturbation-based analyses, where feature grouping may enhance interpretability.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003ePostprandial changes in the plasma metabolome after glucose intake\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe metabolites included in the OGTT data set were mapped onto the metabolic graph depicted in \u003cstrong\u003eFigure 1\u0026nbsp;\u003c/strong\u003e(middle). Among the 634 metabolites included in the OGTT study, only a fraction (25%) overlapped with the full network. Partial coverage (159 metabolites, 14% of the nodes of the network, see green nodes in \u003cstrong\u003eFigure 1\u003c/strong\u003e) is frequently observed in metabolomics studies, due to both limitations in metabolic coverage and network information. The OGTT subset showed uneven representation across communities (see \u003cstrong\u003eFigure 4, top\u003c/strong\u003e) and annotated KEGG pathways (see \u003cstrong\u003eFigure 4, bottom\u003c/strong\u003e), highlighting regions of both strong and limited coverage. Despite this, the subset encompassed functionally relevant modules and pathways, supporting its utility for downstream network-based analyses.\u003c/p\u003e\n\u003cp\u003eFirst, we performed univariate based analysis of each metabolite. A total of 15 metabolites (9.5% of the 159 included in the whole network) showed a significant increase (glucose, fructose, maltose, lactate, glycocholate, glycochenodeoxycholate, and creatine) or decrease (cortisone, ethanolamine phosphate, glycerol, citrulline, xanthine, spermidine, cortisol, and guanidinoacetate) in their postprandial concentrations following glucose intake (t-test p-value\u0026lt;0.05). To identify metabolic pathways significantly altered after glucose intake, pathway analysis was performed using autoscaled data. The global test was selected as the enrichment method, with relative betweenness centrality used as the topology measure, based on the KEGG Homo sapiens library. As shown in \u003cstrong\u003eFigure 5\u003c/strong\u003e, the most significantly affected pathway was \u0026lsquo;starch and sucrose metabolism\u0026rsquo; (FDR = 0.003, impact = 0.50). Additionally, with very low impacts, \u0026lsquo;galactose metabolism\u0026rsquo; (FDR = 0.003, impact = 0.03) and \u0026lsquo;steroid hormone biosynthesis\u0026rsquo; (FDR = 0.02, impact = 0.04) were found altered.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo further evaluate metabolic differences between pre- and post-glucose intake using multivariate analysis, supervised PLS-DA was employed. A 2CV strategy was used for the assessment of the statistical significance of the difference between classes, as described previously. The classification results from the 2CV of PLS-DA are shown in \u003cstrong\u003eFigure 6\u003c/strong\u003e, achieving a cross-validated accuracy of 79%. Statistical significance of the observed separation was evaluated via permutation testing (n = 250), confirming discrimination with p-value \u0026lt; 0.005. Furthermore, regression vectors obtained during the permutation test were used as null distribution to identify 44 metabolites with statistically significant (p-value \u0026lt; 0.05) values in the regression vector of the PLS model built using the true class labels. \u003cstrong\u003eFigure 6\u003c/strong\u003e displays the PLS regression vector and the Variable Importance in Projection (VIP) scores, highlighting the set of 44 metabolites contributing significantly to the class separation. Results from enrichment analysis on this subset using KEGG human metabolic pathways as metabolite set library, indicated as significantly altered the \u0026lsquo;Arginine and proline metabolism\u0026rsquo;, \u0026lsquo;Arginine biosynthesis\u0026rsquo;, and \u0026lsquo;Nicotinate and nicotinamide metabolism\u0026rsquo; pathways.\u003c/p\u003e\n\u003cp\u003eOverall, the univariate analysis identified metabolites exhibiting large individual changes in concentration post-OGTT, highlight selective pathway-level changes particularly in carbohydrate metabolism. In contrast, the multivariate PLS-DA approach, validated by CV and permutation testing, showed broader metabolic effects involving also amino acid metabolism and nicotinate and nicotinamide pathways. Despite these differences, there was a significant overlap between the approaches, as the set of 44 metabolites selected by PLS-DA included the 15 identified as significant by univariate analysis. This divergence between univariate and multivariate findings is consistent with the different statistical sensitivities of the methods: univariate tests are optimized to detect individual effects, whereas multivariate models capture patterns of covariation across multiple metabolites that may not be individually significant[19].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePerturbation-Based Explanations\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo enhance interpretability of metabolic changes underlying the PLS-DA discrimination of samples collected before and after glucose intake, we applied a perturbation-based approach assessing model sensitivity to systematic feature alteration. In this study, feature clustering for perturbation-based explanations was defined at two levels: i) at the pathway level and ii) using communities identified by modularity analysis of a metabolic network. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003ePerturbation-based explanations at the pathway level used sets of features defined in the 35 previously listed metabolic pathways. The second approach classified detected metabolites in the study according to the assigned community from modularity analysis of the metabolic network. \u003cstrong\u003eFigure 7\u003c/strong\u003e shows the distributions of classification accuracies obtained using both methods, where lower predictive performance after permuting than in the model built using true class labels (red dotted line in the figure), indicates that these metabolites collectively contributed significantly to the initial model. Pathway-based perturbation analysis indicated the significance of metabolites included in the \u0026lsquo;Steroid hormone biosynthesis\u0026rsquo; (7), and with lower significance, \u0026lsquo;Starch and sucrose metabolism\u0026rsquo; (3), \u0026lsquo;beta-alanine metabolism\u0026rsquo; (8), and \u0026lsquo;Fructose and mannose metabolism\u0026rsquo; (4) (the number within parenthesis indicate the number of metabolites of these pathways present in the data set), \u0026nbsp;with a single metabolite (D-Fructose) present in more than one of these pathways (see upset plot in \u003cstrong\u003eFigure 8\u003c/strong\u003e).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eOn the other hand, using a perturbation analysis based on modularity-defined communities found two communities whose permutation led to significantly lower predictive performance than in the original model: Communities 13 (10 metabolites), 8 (5 metabolites), and 4 (14 metabolites) (see \u003cstrong\u003eFigure 7\u003c/strong\u003e). As shown in \u003cstrong\u003eFigure 9\u003c/strong\u003e, community 13 included mainly metabolites participating in the \u0026lsquo;Steroid hormone biosynthesis\u0026rsquo; pathway (cholesterol, D-glucuronate, cortisol, cortisone, dehydroepiandrosterone sulfate, urocortisol, cortolone, and etiocholan-3\u0026alpha;-ol-17-one 3-glucuronide) and in the \u0026lsquo;Primary bile acid biosynthesis\u0026rsquo; (cholesterol, 3\u0026beta;,7\u0026alpha;-dihydroxy-5-cholestenoate, and 7\u0026alpha;-hydroxy-3-oxo-4-cholestenoate). Community 8 included metabolites involved in \u0026lsquo;Starch and sucrose metabolism\u0026rsquo; (glucose, fructose, and maltose), \u0026lsquo;Fructose and mannose metabolism\u0026rsquo; (fructose, maltose, mannitol), and \u0026lsquo;Aminosugar and nucleotide sugar metabolism\u0026rsquo; (glucose, fructose, and maltose), as well as \u0026lsquo;Gluconeogenesis\u0026rsquo; (glucose) and \u0026lsquo;Pentose phosphate pathway\u0026rsquo; (glucose). Community 4 showed a more diverse composition including pyruvate and other metabolites participating in several pathways simultaneously such as \u0026lsquo;Cysteine and methionine metabolism\u0026rsquo;, \u0026lsquo;Alanine, aspartate and glutamate metabolism\u0026rsquo;, \u0026lsquo;Glycine, serine and threonine metabolism\u0026rsquo;, \u0026lsquo;Tryptophan metabolism\u0026rsquo; (serotonin, indole-3-acetate, 5-hydroxyindolacetate), as well as \u0026lsquo;Fructose and mannose metabolism\u0026rsquo;, and \u0026lsquo;Gluconeogenesis\u0026rsquo; (lactate), among others.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;While pathway-based perturbation analysis identified well-established metabolic pathways, such as \u0026lsquo;\u003cem\u003eSteroi\u003c/em\u003ed hormone biosynthesis\u0026rsquo;, as important contributors to model performance, its interpretability was limited by overlapping metabolites across pathways. In contrast, the network-based approach grouped metabolites into non-overlapping communities based on metabolic network structure, allowing a more straightforward attribution of predictive relevance. Some communities aligned with known pathways, while others spanned multiple pathways, offering complementary insights into metabolic clusters contributing to model performance. For example, community 13 captured similar biology to the pathway analysis, reinforcing their relevance, while others such as Community 4 represented metabolite groups spanning multiple pathways.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn this study, we propose a network-guided framework for enhancing the interpretability of multivariate metabolomic models through perturbation-based explanations. By using community structures derived from metabolic network topology rather than predefined metabolic pathways, metabolite grouping can be simplified, overcoming redundancy and offering a complementary biological perspective. Application to postprandial metabolic data identified both known and potentially novel functional modules, showing the usefulness of this approach to identify patterns beyond known pathway annotations. However, the approach presents limitations. A partial metabolomic coverage relative to the complete metabolic network may restrict the generalizability of the findings. Besides, further refinement of network construction and community detection methods may also enhance the biological relevance of detected modules. Overall, this study illustrates that integrating network topology into perturbation-based explanations offers a straightforward direction for improving the interpretability of complex multivariate models in metabolomics.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgements\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGQ acknowledges the grant PID2021-125573OB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF A way of making Europe, EU. This work was supported by the Carlos III Health Institute, Ministry of Economy and Competitiveness, Spain [grant numbers CPII21/00003, PI20/00964, and PI23/00202] co-funded by European Regional Development Fund \u0026ldquo;A way to make Europe\u0026rdquo;) and MCIN/AEI/10.13039/501100011033 and, as appropriate, by \u0026ldquo;European Union NextGenerationEU/PRTR\u0026rdquo; [grant number CNS2022-135398]. Authors acknowledge the financial support of projects PID2023-148947OB-I00, RYC2019-026556-I, CNS2023-145528 funded by MCIN/AEI/10.13039/501100011033.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eM. Ivanovs, R. Kadikis, K. Ozols, Perturbation-based methods for explaining deep neural networks: A survey, Pattern Recognit. Lett. 150 (2021) 228\u0026ndash;234. https://doi.org/10.1016/j.patrec.2021.06.030.\u003c/li\u003e\n \u003cli\u003eD. Sidak, J. Schwarzerov\u0026aacute;, W. Weckwerth, S. Waldherr, Interpretable machine learning methods for predictions in systems biology from omics data, Front. Mol. Biosci. 9 (2022) 926623. https://doi.org/10.3389/fmolb.2022.926623.\u003c/li\u003e\n \u003cli\u003eJ. Kuligowski, \u0026Aacute;. P\u0026eacute;rez-Rubio, M. Moreno-Torres, P. Soluyanova, J. P\u0026eacute;rez-Rojas, I. Rienda, D. P\u0026eacute;rez-Guaita, E. Pareja, R. Trullenque-Juan, J.V. Castell, M. Verheijen, F. Caiment, R. Jover, G. 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Hendriks, Reflections on univariate and multivariate analysis of metabolomics data, Metabolomics 10 (2014) 361\u0026ndash;374. https://doi.org/10.1007/s11306-013-0598-6.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"metabolomics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mebo","sideBox":"Learn more about [Metabolomics](http://link.springer.com/journal/11306)","snPcode":"11306","submissionUrl":"https://submission.nature.com/new-submission/11306/3","title":"Metabolomics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"metabolomics, multivariate analysis, perturbation-based explanations, interpretability, network analysis","lastPublishedDoi":"10.21203/rs.3.rs-6742815/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6742815/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Multivariate modeling is crucial for uncovering complex patterns in metabolomic data, yet the interpretability of such models remains a major challenge. Here, we propose a network-guided framework that enhances perturbation-based explanations by grouping metabolites according to communities identified in metabolic networks, rather than relying on predefined pathways. Applied to postprandial plasma metabolomic data as a model example, the method revealed both established and novel functional modules relevant to glucose metabolism. The use of metabolite communities derived from network representation in perturbation-based models serves as a complementary tool for the biochemical interpretation of multivariate models, extending beyond fixed, stablished pathways. The strategy is model-agnostic and readily transferable across omics domains, offering a robust tool for improving model interpretability and hypothesis generation in complex biological datasets.","manuscriptTitle":"Enhancing Interpretability in Multivariate Metabolomic Modeling through Network-Guided Perturbation-Based Explanations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-30 16:08:27","doi":"10.21203/rs.3.rs-6742815/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-18T13:18:30+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-05T16:54:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"212880219753217415939341769808316502295","date":"2025-07-09T08:34:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"176395027875111127974812170791058723403","date":"2025-07-08T02:22:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-07T08:16:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"125137359438775709867123596735521185095","date":"2025-05-29T21:38:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-28T09:44:53+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-27T09:14:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-27T09:13:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Metabolomics","date":"2025-05-25T09:03:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"metabolomics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mebo","sideBox":"Learn more about [Metabolomics](http://link.springer.com/journal/11306)","snPcode":"11306","submissionUrl":"https://submission.nature.com/new-submission/11306/3","title":"Metabolomics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"be2aa948-7cf2-4ccd-8a46-d9cdc3c3e1e7","owner":[],"postedDate":"May 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-09-29T15:59:09+00:00","versionOfRecord":{"articleIdentity":"rs-6742815","link":"https://doi.org/10.1007/s11306-025-02347-8","journal":{"identity":"metabolomics","isVorOnly":false,"title":"Metabolomics"},"publishedOn":"2025-09-26 15:57:05","publishedOnDateReadable":"September 26th, 2025"},"versionCreatedAt":"2025-05-30 16:08:27","video":"","vorDoi":"10.1007/s11306-025-02347-8","vorDoiUrl":"https://doi.org/10.1007/s11306-025-02347-8","workflowStages":[]},"version":"v1","identity":"rs-6742815","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6742815","identity":"rs-6742815","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}