Introduction

Cancer comprises a heterogeneous group of diseases driven by diverse genetic and epigenetic alterations that promote malignant phenotypes such as uncontrolled proliferation, resistance to cell death, and immune evasion1,2. These alterations frequently disrupt key signalling pathways that regulate proliferation and apoptosis, leading to sustained growth signals and impaired cell death mechanisms2. Signalling deregulation also drives downstream metabolic changes. Cancer cells reprogramme their metabolism to meet the demands of rapid growth by producing energy and biosynthetic precursors3,4. Pathways such as PI3K/AKT/mTOR, MAPK, and TAK1/NF-κB contribute to this metabolic rewiring and play central roles in oncogenesis5,6. High-throughput technologies have transformed our understanding of cancer by providing detailed molecular profiles7. However, the complexity of cancer progression and treatment response remains only partially understood. Bioinformatic methods—such as differential expression, over-representation, and gene set enrichment analyses—have been widely used to identify changes in gene activity after perturbations8,9. While informative, these approaches are typically descriptive and do not simulate underlying cellular dynamics10.

Mathematical models can help bridge the gap between molecular interactions and phenotypic outcomes by providing mechanistic insights11. Boolean models of cell signalling have been developed for various cancer types and used to predict cell fate and the effects of perturbations such as drug treatments12,13. These models have also been tailored with omic data to improve predictions of treatment outcomes14 and to identify synergistic drug combinations across different cancers15,16. In the context of cancer metabolism, genome-scale metabolic models (GEMs) have been reconstructed for humans17,18,19 and model organisms such as rats20. Constraint-based methods21 have enabled the integration of omic data into these models to generate context-specific GEMs (CS-GEM)22,23,24. CS-GEM has been applied to cancer cells25 to investigate metabolic reprogramming26, identify potential therapeutic targets27,28, and screen for anti-metabolites29. However, the construction of CS-GEM remains challenging due to methodological inconsistencies and a lack of consensus on best practices30,31. To address these limitations, alternative approaches such as genetic minimal cut sets32 have been employed to predict synthetic lethal interactions33,34. Additionally, constraint-based algorithms like tasks inferred from differential expression (TIDE)35 and CellFie36 have been developed to infer pathway activity directly from gene expression data, without the need to construct a full GEM.

In previous work, Flobak et al. constructed a Boolean model of signalling in the gastric adenocarcinoma cell line AGS and identified synergistic effects of kinase inhibitor combinations, which were validated in vitro15. Tsirvouli et al. later expanded on these findings using transcriptomic and phosphoproteomic profiling across time points to dissect the mechanisms of synergy37. This work aimed to characterise the metabolic alterations induced by three kinase inhibitors and their synergistic combinations in AGS cells. We profiled gene expression changes following drug treatments and used constraint-based modelling to investigate their metabolic effects. Specifically, we applied the TIDE algorithm35 to infer changes in metabolic pathway activity and proposed a variant named TIDE-essential, which focuses on essential genes without relying on flux assumptions. To quantify synergy at the metabolic level, we introduced a scoring scheme that compares the effects of combination treatments with those of individual drugs. This enabled us to identify metabolic processes specifically altered by drug synergies. We implemented both TIDE and TIDE-essential in an open-source Python package and command-line tool, MTEApy, to facilitate broader use. Our approach provides a framework for investigating drug-induced metabolic rewiring and offers insights into the mechanisms of synergy in targeted cancer therapies.

Results

AGS cells treated with kinase inhibitors show larger numbers of up-regulated than down-regulated genes

Kinase inhibitors are known to down-regulate pathways involved in proliferation and survival while up-regulating stress response and compensatory mechanisms. Furthermore, combining kinase inhibitors can produce synergistic effects that are absent with individual drugs. In this study, we investigated the functional impact of synergistic drug combinations on various cellular processes, with a particular emphasis on cellular metabolism. We performed a transcriptomic analysis of AGS cells treated with the kinase TAK1, MEK, and PI3K inhibitors (TAKi, MEKi, PI3Ki) and two PI3Ki combinations (PI3Ki–TAKi and PI3Ki–MEKi) and without inhibitors (control condition). We sequenced the transcriptome of AGS cells for the different conditions and identified differentially expressed genes (DEGs) using a standard pipeline with the DESeq2 package38 (see the “Methods” section). Results showed that the number of DEGs varied across treatment conditions, with an average of ~2000 DEGs per condition (see Fig. 1A and B left panels and Supplementary Data 1). We observed a larger number of up-regulated or over-expressed genes (~1200) than down-regulated (~700) across all treatment conditions. We focused specifically on metabolic genes and found that the patterns remain, suggesting that drugs induce the activity of different metabolic processes (see Fig. 1A and B, right panels). The analysis also reveals that MEKi induces the most significant transcriptional changes among individual treatments, followed by TAKi and PI3Ki (see Fig. 1A). Regarding the combinatorial treatments, in PI3Ki–TAKi, the number of DEGs is similar to the one observed for TAKi. Nonetheless, the number of DEGs in PI3Ki–MEKi was mildly higher than those reported in either PI3Ki or MEKi, suggesting a possible synergetic effect (see Fig. 1A).

Fig. 1: Differential expression analysis on AGS cells after drug perturbations reveals significant shifts.
figure 1

A Bar chart indicating the number of differentially expressed genes (DEGs) up- and down-regulated per treatment condition for all genes (left panel) and genes within the metabolic model Human-GEM (right panel). Significance was set using an adjusted p-value of <0.05, and an absolute log-FC > 1. B Scatter plots showing the distribution of DEGs across treatments for all genes (left panel) and genes within the metabolic model Human-GEM (right panel). The median is indicated using a red, horizontal line. C Venn diagrams for up- (left panel) and down-regulated (right panel) DEGs for the TAKi, PI3Ki and PI3Ki–TAKi treatments. D Venn diagrams for up- (left panel) and down-regulated (right panel) DEGs for the MEKi, PI3Ki and PI3Ki–MEKi treatments. Darker colours indicate a higher number of DEGs.

Full size image

We assessed the similarity of up- and down-regulated DEGs across treatment conditions using the Jaccard Index (JI). Shared DEGs may reflect common transcriptional responses, while combination-specific DEGs may suggest drug-specific mechanisms; in particular, changes only observed in the combinatorial treatments may indicate potential synergistic effects. The analysis shows that PI3Ki–TAKi predominantly exhibits an additive effect, with only a small proportion (~15%) of unique DEGs not observed in single treatments (see Fig. 1C and Supplementary Fig. 1). In contrast, PI3Ki–MEKi demonstrates potentially stronger synergistic effects, evidenced by a larger number of DEGs and a higher proportion (~25%) of unique DEGs (see Fig. 1D and Supplementary Fig. 1). These unique DEGs may represent distinct pathways activated by the combined effect of drugs and thus may provide insight into the mechanisms of synergies.

To explore the functional implications of the observed gene expression changes, we performed a gene set enrichment analysis using the Gene Ontology database (see the “Methods” section for details). The analysis revealed no strong bias in gene set regulation, with ~55% down-regulated and 45% up-regulated gene sets on average across conditions (Fig. 2A and B). An exception was observed for PI3Ki–TAKi, which exhibited a significantly larger proportion of down-regulated gene sets (Fig. 2A). Interestingly, this pattern contrasts with the overall gene expression changes, where up-regulated genes predominated across conditions (Fig. 2A). Among individual treatments, MEKi induced the most significant perturbation in GO biological processes (n = 142), followed by TAKi (n = 74) and PI3Ki (n = 40), consistent with the trends observed in the differentially expressed genes (DEGs).

Fig. 2: Gene Ontology gene set enrichment analysis summary.
figure 2

A Bar chart indicating the number of significant gene sets up- and down-regulated per treatment condition. Significance was set using an adjusted p-value of <0.05, and an absolute normalised enrichment score (NES) > 1. B Scatter plot showing the distribution of DEGs across treatments for all genes. The median is indicated using a red, horizontal line. C and D Heatmaps of the top 15 significant gene sets in terms of significance and NES across all treatment conditions for up- and down-regulated gene sets, respectively. Bluer colours in the heatmap indicate lower, negative NES values, while redder colours indicate higher, positive NES values. White cells indicate that the specific gene set in a given condition was not statistically significant.

Full size image

We first focus on those processes that are found to be significantly affected in all the conditions. The results show down-regulation of rRNA and ncRNA ribonucleotide biogenesis, rRNA–protein complex organisation, and tRNA aminoacylation, suggesting an overall suppression of protein synthesis and translational machinery in the treated cells; down-regulation of mitochondrial gene expression is also found in all the conditions (see Supplementary Fig. 2A). Furthermore, we also observed the up-regulation of processes related to the major histocompatibility complex and the transport of organic hydroxy compounds. Cells treated with the individual drugs exhibit similar down-regulation patterns, primarily affecting pathways related to DNA processes, keratinocyte development, and apoptosis (see Fig. 2C). Regarding the up-regulated process, we observed common pathways including metabolism, immune-related processes (e.g., interferon signalling), and condition-specific changes such as lipid metabolism (TAKi) and nervous system development (PI3Ki). Notably, TAKi and PI3Ki display more similar patterns to each other than to MEKi (see Fig. 2D and Supplementary Fig. 2A). Additionally, we performed the same analysis using pathway-related gene sets from the Kyoto Encyclopaedia of Genes and Genomes (KEGG) database. The results were consistent with those obtained using Gene Ontology terms, revealing down-regulation of key processes such as NF-κB signalling, amino acid biosynthesis, aminoacyl-tRNA synthesis, and ribosome biogenesis (see Supplementary Fig. 2B).

We selected the 15 most significant altered gene sets observed in the combinatorial treatments and found that almost all are also altered in the individual treatment counterparts. Nevertheless, we observed some potential synergetic effects in both combinations that include the down-regulation of keratinisation and the regulation of mRNA metabolic process. Next, we focus on those pathways that are significantly altered in the combinatorial treatments but not in the individual drug treatments (see Supplementary Fig. 3). We identified 55 condition-specific gene set alterations in the PI3Ki–MEKi condition, accounting for ~40% of all gene sets altered in this condition. For the PI3Ki–TAKi condition, 12 condition-specific gene set alterations were observed, representing around 30% of the significant deregulated gene sets (see Supplementary Fig. 3). We analysed the different gene sets altered in the combinatorial treatments and found that the altered processes represent broad functional categories and do not include specific metabolic processes. Therefore, we propose using a model-driven inference approach to gain deeper insight into the specific metabolic processes altered by the synergistic effects of the drug combinations.

Kinase inhibitors induce down-regulations in key biosynthetic metabolic pathways

Cell growth and proliferation require energy and building blocks that are supplied by different metabolic pathways. Therefore, drugs that affect cell proliferation are likely to have a downstream inhibitory effect on the activity of various metabolic pathways. Herein, we used a constraint-based metabolic modelling approach to better understand the changes in metabolic pathway activity following treatment with kinase inhibitors. Specifically, we used the Task Inferred from Differential Expression (TIDE) framework, proposed by Dougherty et al. (2021)35 to find metabolic pathways significantly altered in the different conditions (see the “Methods” section). We retrieved the most recent version of the genome-scale metabolic reconstruction of human cells, the Human-GEM model19. We also retrieved a list of 195 previously published metabolic tasks36, which is already included in the Human-GEM model repository19. We manually curated several tasks that were found to be infeasible with the Human-GEM model, resulting in a final list of 187 consistent tasks. This curated list was used for the remainder of the analysis (see the “Methods” section and Supplementary Data 2 for details).

We ran TIDE on all the conditions using the Human-GEM model and a list of 189 metabolic tasks. The results showed that, on average, ~50 metabolic tasks were significantly altered in each treatment condition. A total of 30, 17, and 77 significant metabolic tasks were identified in the individual treatments TAKi, MEKi, and PI3Ki; whereas 55 and 66 were identified in the combinatorial treatments PI3Ki–TAKi and PI3Ki–MEKi, respectively (see Fig. 3A and Supplementary Data 3). We observed a trend towards down-regulation of metabolic tasks, with ~5 and ~40 up- and down-regulated metabolic tasks, respectively, on average across all treatment conditions (see Fig. 3A). This pattern contrasted with the differential expression results, where we observed more up-regulated DEGs (see Fig. 1A) and is similar to the trends exhibited by the GSEA results (see Fig. 2A).

Fig. 3: Significant metabolic shifts were identified in AGS cells after drug treatment.
figure 3

A Bar chart indicating the number of significant metabolic scores up- and down-regulated per treatment condition. Significance was set using a p-value of <0.025. B Jaccard index correlation plots between down- (left panel) and up-regulated (right panel) metabolic tasks across treatment conditions. Rows and columns were clustered using Ward’s method. Darker hues indicate higher Jaccard index correlation values. C Bar chart indicating the proportions of metabolic systems altered in each condition. D Heatmap of shared metabolic pathways significantly altered across all the treatments. Darker hues indicate lower, negative metabolic scores. The metabolic system is indicated on the colour strip to the left of the rows.

Full size image

We assessed the similarities between treatment conditions using the Jaccard Index for the up and down-regulated metabolic perturbations (see Fig. 3B). The highest JIup was reported between the two conditions that identified the most up-regulated perturbations, TAKi and PI3Ki–TAKi, while other conditions had fewer up-regulated perturbations and therefore, lower JIup values. This result indicates that TAK1 inhibition triggers the up-regulation of some metabolic pathways that are also up-regulated in the combinatorial treatment with PI3Ki. Regarding down-regulated perturbations, PI3Ki and PI3Ki–MEKi displayed the highest similarity values, followed by PI3Ki and PI3Ki–TAKi.

In general, metabolic changes were mainly observed in pathways related to amino acids, carbohydrates, lipids, and nucleotide metabolism (see Fig. 3C). We first analysed pathways affected in all the conditions and found that several metabolic tasks, such as the synthesis and conversion of some amino acids and the production of some nucleotides and deoxynucleotides, were consistently downregulated across all conditions (see Fig. 3D). The results also showed that the conversion of aspartate to asparagine and serine synthesis were down-regulated across all treatment conditions. Notably, we observed that in PI3Ki, or any of its combinations, more amino acid perturbations were identified than in any other single treatment.

Synergistic metabolic shifts in AGS cells were identified following combinatorial drug treatments

The TIDE results showed that most of the metabolic changes identified in the individual treatments are also observed in the combinatorial treatments. However, we also found several examples of metabolic processes exhibiting changes only in the combinatorial treatments. We focused on these unique metabolic perturbations, since they may represent synergetic effects. We introduced a simple scoring system to identify the presence of potential weak and strong synergistic effects in the regulation of metabolic pathways. We considered weak synergies cases where the metabolic score in combinatorial treatments is higher/lower than the maximum/minimum observed in their single-drug conditions. Conversely, we defined strong synergies as cases where individual drugs show no effect on the expression of metabolic processes, while the combinatorial treatment significantly alters the process. Noting A and B as two individual treatments, AB as their combination, t as a given metabolic task, and MS(A, t) as the corresponding metabolic score of task t in the condition A, we defined weak synergies as follows:

$$\begin{array}{ll}\quad\,\,{\rm{Up}}{\hbox{-}}{\rm{regulated}}:\quad {{MS}}(AB,t)\,>\,{{max}}({{MS}}(A,t),\,{{MS}}(B,t))\\ {\rm{Down}}{\hbox{-}}{\rm{regulated}}:\quad {{MS}}(AB,t)\,<\,{{min}}({{MS}}(A,t),\,{{MS}}(B,t))\end{array}$$
(1)

and a strong synergy is defined by the following expression:

$$\begin{array}{ll}\quad\,\,{\rm{Up}}{\hbox{-}}{\rm{regulated}}:\quad {{MS}}(AB,t)> 0\,\,\& \,\left({{MS}}(A,t)=0\,\& \,{{MS}}(B,t)=0\right)\\ {\rm{Down}}{\hbox{-}}{\rm{regulated}}:\quad{{MS}}(AB,t)< 0\,\,\& \,\left({{MS}}(A,t)=0\,\& \,{{MS}}(B,t)=0\right)\end{array}$$
(2)

In the PI3Ki–TAKi condition, we found that 14 out of 55 significantly altered metabolic processes exhibit some kind of synergistic effect (see Fig. 4A and Supplementary Data 4). On the other hand, the PI3Ki–MEKi combination exhibited a higher value of synergetic perturbation, including 49 out of 66 significantly affected pathways (see Fig. 4A). Interestingly, both non-synergistic and synergistic perturbations observed in the PI3Ki–TAKi and PI3Ki–MEKi treatments show a bias towards down-regulation or inhibition of metabolic processes (see Supplementary Data 3 and 4). In addition, there were no differences reported between non-synergistic and synergistic metabolic scores in PI3Ki–TAKi (Mann–Whitney test p-value = 0.363), but some slightly significant differences were reported between scores in PI3Ki–MEKi (p-value = 0.043) (see Fig. 4B). Most of the synergistic perturbations in PI3Ki–TAKi included pathways related to the lipid (n = 5) and amino acid (n = 4) metabolism (see Fig. 4C and D). In PI3Ki–MEKi, however, apart from the aforementioned systems (n = 8 and n = 25, respectively), synergistic perturbations were also observed in the nucleotide (n = 10) and carbohydrate (n = 5) metabolism, among others (see Fig. 4C and D).

Fig. 4: Synergistic effects over AGS metabolism trend towards down-regulation.
figure 4

A Bar charts indicating the number of significant and synergistic metabolic tasks identified with TIDE in PI3Ki–TAKi and PI3Ki–MEKi. Synergy type is indicated in blue for down-regulated scores and in red for up-regulated. Non-synergistic and non-significant results are indicated in grey. B Distribution of significant metabolic scores between non-synergistic and synergistic metabolic tasks identified with TIDE in PI3Ki–TAKi and PI3Ki–MEKi. The mean is indicated with a horizontal, red line. P-values were obtained using a Mann–Whitney test. C Heatmap of strong synergies for either PI3Ki–TAKi or PI3Ki–MEKi. Scores for all treatment conditions are shown for comparison. Coloured bars indicate the metabolic system (leftmost) and the combinatorial treatment to which the synergy belongs. Panel D shows a heatmap of weak synergies for either PI3Ki–TAKi or PI3Ki–MEKi. Scores for all treatment conditions are shown for comparison. Coloured bars indicate the metabolic system (leftmost) and the combinatorial treatment to which the synergy belongs.

Full size image

Strong synergies regarding the PI3Ki–TAKi treatment involved the down-regulation of the presence of the thioredoxin system through the thioredoxin reductase activity and some alterations in the phenylalanine and tryptophan metabolism. Pathways related to lysine metabolism and degradation of cis-vaccenic acid were slightly up-regulated in PI3Ki–TAKi (see Fig. 4C). Interestingly, all strong synergies involved in PI3Ki–MEKi were found to be down-regulated, and included a wide range of processes from ornithine and aspartate biosynthesis, gluconeogenesis, and deoxynucleotides to ubiquinone 10 (Q10) biosynthesis. Regarding weak synergies, more perturbations were observed in PI3Ki–MEKi than in PI3Ki–TAKi, and only 2 were identified as up-regulated across treatment conditions. Interestingly, four weak synergies were common to PI3Ki–TAKi and PI3Ki–MEKi conditions: glycerol-3-phosphate synthesis, hydroxymethylglutaryl-CoA synthesis, and acetone and acetoacetate synthesis.

The TIDE-essential framework identifies new metabolic perturbations and synergistic effects in AGS metabolism

In this section, we introduced a variation of the TIDE algorithm, named TIDE-essential, that aims to extend the framework (see the “Methods” section for more details). In the TIDE algorithm, each metabolic task, defined by a set of input and output metabolites, is first associated with a feasible flux distribution. Due to the presence of isozymes or alternative pathways, a metabolic task may have multiple flux distributions that fulfil its requirements. TIDE resolves this by using parsimonious Flux Balance Analysis (pFBA) to compute a single flux distribution that minimises total flux while satisfying the task constraints (see the “Methods” section). The activity change of the pathway is then estimated by projecting gene expression changes (log-fold changes) onto the flux-carrying reactions of this reference solution. However, because this flux distribution is computed before integrating gene expression data, it may not reflect the biologically relevant flux patterns under perturbed conditions. To assess whether the reference flux distributions for each task were unique or potentially variable, we performed flux variability analysis (FVA) across all 187 tasks (see the “Methods” section). We found that 149 of them exhibit alternative optimal flux distributions (Supplementary Data 5), indicating that reliance on a single reference flux may introduce bias in the results.

To address this potential bias, we propose a variation of the TIDE algorithm that does not rely on a precomputed flux distribution. Instead, it evaluates task activity based solely on the set of essential genes required to perform each metabolic task (Supplementary Fig. 4). These essential genes are identified through in-silico single-gene knockout analysis using flux balance analysis (FBA), and represent that are necessary, but not necessarily sufficient, to convert the specified input metabolites into the corresponding outputs (see the “Methods” section). The rationale for focusing on essential genes is that they represent non-redundant components in the metabolic network, making them likely points of regulatory control, and therefore, changes in the expression of such genes are more likely to reflect changes in the capacity to perform a specific task. After identifying essential genes for each task, we compute the aggregate expression change of these genes and assess its statistical significance using the same empirical null model applied in TIDE.

This essential-gene-based formulation of TIDE complements and extends the analysis of metabolic perturbations for two main reasons: (i) it eliminates the dependency on pFBA-derived flux distributions to identify task-associated reactions and (ii) it operates directly at the gene level, increasing interpretability and relevance in transcriptomics-based analyses. While this strategy may have lower coverage—since not all tasks have essential genes or have only a few—it offers an alternative perspective that does not rely on a predefined flux solution. As such, TIDE-essential provides an additional line of evidence for tasks where essential genes are identified, and the two methods can be used together to increase confidence in the inferred metabolic changes.

We applied TIDE-essential to the same set of 187 metabolic tasks and treatment conditions analysed with TIDE. Across all conditions, TIDE-essential identified 69 significantly altered tasks, of which 40 overlapped with those detected by TIDE (Fig. 5A). Moreover, the metabolic scores produced by the two methods were highly correlated (Spearman’s ρ = 0.93; Fig. 5B), indicating a strong overall agreement. Despite this consistency, TIDE generally identified a larger number of altered tasks compared to TIDE-essential (see Table 1, Supplementary Data 6 and Supplementary Fig. 5). For example, under PI3Ki treatment, TIDE identified 77 altered tasks, whereas TIDE-essential identified only 10. A similar trend was observed across the other treatment conditions. Importantly, however, TIDE-essential was able to detect both a meaningful subset of overlapping perturbations and a small number of unique task alterations not captured by TIDE. In the MEKi condition, for instance, TIDE and TIDE-essential shared 7 common altered tasks, while each method uniquely identified 10 and 9 tasks, respectively. This pattern indicates that TIDE-essential complements TIDE by identifying condition-specific changes that the flux-based variant might miss.

Fig. 5: New metabolic perturbations and synergistic effects in AGS metabolism can be inferred using TIDE-essential.
figure 5

A Venn diagram showing the overlap of significant metabolic tasks between the TIDE and TIDE-essential framework across treatment conditions. B Scatter plot of the metabolic scores for the shared tasks between TIDE and TIDE-essential. The horizontal grey line corresponds to a fitted linear model, with a Spearman rank correlation value of ρ = 0.93 (p-value < 1−10). C Heatmap of all significant tasks identified by TIDE-essential in PI3Ki–TAKi and PI3Ki–MEKi. Redder hues indicate higher, positive metabolic scores, and bluer ones indicate lower, negative values. The metabolic subsystem is indicated on the colour strips on the left of the rows. A brief description of whether a metabolic task is newly identified (green hues) or shared with TIDE (orange hues), and whether a synergy effect is newly identified or re-classified from TIDE for PI3Ki–TAKi and PI3Ki–MEKi is indicated on the colour strips to the left of the rows.

Full size image
Table 1 Tasks detected by TIDE and TIDE-essential in each condition
Full size table

TIDE-essential identified 11 and 18 down-regulated metabolic tasks in the PI3Ki–TAKi and PI3Ki–MEKi combination treatments, respectively, revealing the same trend toward down-regulation, in line with previous observations (Fig. 5C). Notably, in the PI3Ki–TAKi condition, TIDE-essential detected five metabolic tasks not reported by TIDE, including three associated with strong synergy (Fig. 5C). Among these, beta-alanine synthesis was down-regulated, while glycan degradation was broadly up-regulated. In contrast, homocysteine synthesis was up-regulated and cysteine synthesis down-regulated, though neither was linked to synergistic effects (Fig. 5C and Supplementary Data 6). In the PI3Ki–MEKi condition, TIDE-essential uncovered four new perturbations, two of which displayed strong synergy, namely, the down-regulation of beta-alanine synthesis and a phosphatidylinositol conversion (Fig. 5C). Furthermore, glycan degradation was up-regulated and gamma-linolenate degradation was down-regulated, although these changes were not classified as synergistic.

Discussion

In this study, we explored the functional and metabolic effects of individual kinase inhibitors and their synergistic combinations in a cancer cell line. We observed a general trend of gene overexpression across all treatment conditions. Although individual gene expression levels showed an overall trend of overexpression, pathway-level analysis revealed the opposite effect, suggesting that transcriptional changes may be part of a broader regulatory compensation mechanism. This underscores the importance of integrating gene-level data with pathway and metabolic models to reveal biologically meaningful responses.

GSEA results showed that several gene sets related to metabolic processes were down-regulated after treating the cells. However, these results lacked pathway-level resolution, making it difficult to infer precise functional consequences. For instance, the gene set associated with amino acid metabolism identified in GSEA does not specify which particular amino acids are affected, nor does it clarify whether the altered pathway relates to biosynthesis or degradation. Similar results were found for other functional categories, such as lipid and nucleotide metabolism. We also repeated the analysis using pathway-specific gene sets from the KEGG database and found similar results. Although GSEA remains a widely used and powerful tool for enrichment analysis, its application in metabolic studies can be constrained by the granularity of the gene sets. Even with curated, metabolism-specific gene sets, GSEA does not incorporate biochemical constraints such as reaction stoichiometry, isoenzyme usage, or multi-subunit enzyme complexes. In contrast, model-based approaches like TIDE and TIDE-essential leverage genome-scale metabolic models and their gene–protein-reaction rules to capture these mechanistic dependencies and physicochemical constraints, enabling a more functionally grounded inference of metabolic activity. We emphasise that this is not an inherent limitation of the GSEA algorithm, but rather a result of its design, which operates solely at the level of gene sets without incorporating the biochemical and structural constraints. This distinction is particularly relevant when analysing gene expression of metabolic processes, where model-based approaches provide complementary insights that extend beyond what can be inferred from gene-level enrichment alone.

We integrated the differential gene expression results into the genome-scale metabolic model of human cells using the TIDE algorithm to identify metabolic pathways altered under different treatment conditions. The results revealed significant down-regulation of several metabolic pathways, particularly those involved in nucleotide synthesis, amino acid metabolism, and lipid biosynthesis. We also developed TIDE-essential, a variant of TIDE that uses only task-essential genes and bypasses the need for flux distributions when estimating pathway activity. The comparison of the approaches showed that TIDE consistently detects more altered tasks (e.g., 77 vs. 10 for PI3Ki), reflecting its higher sensitivity. However, TIDE-essential captures a meaningful subset of overlapping perturbations (e.g., 7 shared tasks for PI3Ki) and identifies additional unique ones (e.g., 9 unique tasks for MEKi). These findings indicate that the two algorithms are complementary and that TIDE-essential can broaden the coverage of detectable perturbations, especially in cases where flux-based approaches may be limited or less interpretable at the gene level. Importantly, focusing on genes that are essential for metabolic tasks further increases confidence that their dysregulation would lead to functional consequences at the cellular level.

Using these complementary model-based approaches, we identified several metabolic pathways that may be affected by drug treatments and combinations at the metabolic level. In particular, nucleotide synthesis pathways (including IMP, GTP, and dATP) were down-regulated across all treatment conditions, with the most pronounced effects observed in the PI3Ki–MEKi combination. A reduced supply of DNA and RNA building blocks is likely linked to the decreased cell proliferation observed in AGS cells. These findings are consistent with previous studies reporting diminished nucleotide biosynthesis and down-regulation of aminoacyl-tRNA synthetase enzymes under similar conditions37.

In general, we found that treatments involving PI3Ki consistently exhibited a stronger inhibition of metabolic pathways than the other conditions, especially regarding amino acid metabolism. These results are in agreement with previous studies highlighting the central role of the PI3K/AKT/mTORC1 pathway in cancer metabolism5. Notably, the conversion of aspartate to asparagine was found to be the top down-regulated metabolic task across all treatment conditions, with the most pronounced effect observed in cells treated with PI3Ki. The PI3K/AKT/mTORC1 signalling pathway is known to positively regulate asparagine production39, which aligns with our observation of enhanced down-regulation in conditions involving PI3Ki and its combinations. Furthermore, the inhibition of asparagine synthetase has been shown to enhance sensitivity to metabolic stress39, which may contribute to the observed reduction in AGS cell proliferation.

With the introduction of a methodology to identify the presence of synergies in metabolic pathways, we have obtained relevant results related to the synergistic effects of drug combinations in cellular metabolism. The results indicated that the PI3Ki–MEKi combination had a more pronounced synergistic effect on metabolic pathways compared to the PI3Ki–TAKi combination, as evidenced by a greater number of synergistic alterations, particularly in pathways involving cofactors and vitamins. This aligns with in-vitro assays indicating that the PI3Ki–MEKi combination is more effective in reducing cell proliferation than the PI3Ki–TAKi combination15.

The strong synergistic effect observed in PI3Ki–MEKi is likely due to the inhibition of pathways not altered by the individual drugs. For instance, we found that the synthesis of spermidine is only observed down-regulated in PI3Ki–MEKi. Polyamines are essential for DNA stability, cell proliferation, and stress resistance40, and their depletion has been linked to increased DNA damage and apoptosis41,42,43. We also found that ubiquinone (CoQ) synthesis was strongly down-regulated in PI3Ki–MEKi, specifically through reduced expression of coenzyme Q3 methyltransferase (COQ3). COQ3 expression has recently been reported to be associated with worse patient survival in oesophageal adenocarcinoma44, thus a down-regulation in this metabolic pathway could potentially hinder cancer progression in AGS cells as well.

The PI3Ki-TAKi condition exhibited less synergetic effects in the metabolic pathways than PI3Ki–MEKi. Nevertheless, we found that PI3Ki-TAKi induced a down-regulation in the thioredoxin pathway, suggesting a strong synergistic effect. Thioredoxin protein levels are implicated in tumour growth and apoptosis inhibition45, and recently, thioredoxin has been proposed as a therapeutic target in lung cancer for its ability to increase sensitivity to CHK1 inhibitors46. We also identified a down-regulation in the synthesis of quinolinate from tryptophan, a pathway that has been associated with cell death and cell cycle arrest in colorectal cancer models47.

This study lays the foundation for further exploration of transcriptionally driven metabolic changes in cancer cells through the integration of constraint-based modelling and transcriptomics. Nonetheless, several methodological limitations should be acknowledged. First, all kinase inhibitor treatments were applied at fixed concentrations (GI50), which standardises toxicity levels across drugs and facilitates comparison of their metabolic effects. However, this design does not fully capture the nonlinear, dose-dependent nature of transcriptomic and metabolic regulation. Incorporating a range of drug concentrations or full dose–response curves in future studies could provide a more comprehensive view of how these pathways are perturbed under different levels of inhibition. Second, we used a simplified statistical model in DESeq2 with treatment condition as a categorical variable. While this choice aligns with the experimental design—using GI50 concentrations for single drugs and half-dose combinations to maintain equitoxicity—it limits the incorporation of interaction terms that are typically used to model synergistic effects. Adding such terms would complicate the interpretation of log fold-changes, particularly for combinatorial treatments. Future studies with expanded experimental designs could explore interaction effects more explicitly and allow for more robust modelling of drug synergy at the transcriptomic and metabolic levels.

By integrating transcriptomic data using TIDE and TIDE-essential, we provide a systematic framework for uncovering metabolic responses to drug treatments by leveraging the use of GSMMs. We identified specific pathways down-regulated exclusively by synergistic combinations by analysing metabolic alterations induced by single drugs and synergistic combinations. These findings offer insight into the molecular basis of drug synergies and reveal metabolic vulnerabilities that could be exploited as novel therapeutic targets. While our results suggest meaningful biological consequences at the metabolic level and provide new grounds for future work, the experimental validation of the results is beyond the scope of this study. Finally, to enhance reproducibility and facilitate adoption, we have implemented the TIDE and TIDE-essential algorithms in the open-source Python package MTEApy, offering an accessible tool for the metabolic modelling community. This framework readily applies to other cancer types and drug combinations, supporting broader applications in precision oncology.

Methods

Experimental setup

Cell culture and drug treatments

AGS (human gastric adenocarcinoma, ATCC, Rockville, MD) were grown in Ham’s F12 medium (Invitrogen, Carlsbad, CA) supplemented with 5% foetal calf serum (FCS; Euroclone, Devon, UK) and 10 U/ml penicillin–streptomycin (Invitrogen). AGS cells were seeded in six-well plates and treated after 24 h with kinase inhibitors (5Z)-7-oxozeaenol (TAKi), PD0325901 (MEKi), and PI103 (PI3Ki), individually or in combination, for another 24 h. Chemical inhibitors (5Z)-7-oxozeaenol, PD0325901, and PI-103 (all Merck) were dissolved in DMSO at stock concentrations of 20 mM. Each drug treatment was administered at concentrations previously reported to reduce growth by 50% (GI50 concentrations) after 48 h compared to the vehicle control, dimethyl sulfoxide (DMSO)15. Cells were also treated using the combination of these drugs (i.e., PI3Ki–TAKi and PI3Ki–MEKi) that were experimentally confirmed to be synergistic in AGS cells15. For the combinatorial treatments, the half concentrations of GI50 were used for each drug (see Table 2).

Table 2 Description of the kinase inhibitor used
Full size table

RNA sequencing

After treatment, cells were lysed in RNA lysis buffer (Qiagen RLT Plus) and stored at −80 °C. RNA extraction was performed using the AllPrep DNA/RNA/miRNA Universal Kit (Qiagen). RNA concentration and integrity were assessed using the Qubit RNA HS Assay and Agilent Bioanalyzer, respectively. Libraries were prepared with the Illumina Stranded mRNA Prep Ligation Kit, purified with AMPure XP beads, quantified via qPCR, and validated on a Bioanalyzer. Sequencing (2 × 64 bp) was performed on an Illumina HiSeq2000 platform. For each treatment condition and the control, four replicates were performed.

Bioinformatic analysis

RNA-Seq data processing and quantification

FASTQ files were generated with bcl2fastq (v2.20), quality-checked with fastqc (v0.12.1), and preprocessed using fastp (v0.20.1). Transcript abundances were estimated using Salmon (v1.10.3) with the reference Human genome GRCh38. Quality control summaries were generated using MultiQC (v1.23), and gene-level counts were computed using the tximport R package (v1.32.0).

Differential expression analysis

Differential expression analysis (DEA) was performed using the DESeq2 framework (version 1.40.0)38. A model was fitted for each gene using a categorical variable with different levels as the treatment conditions, and adjusting for the replicate number. The DMSO samples were used as the baseline for all pair-wise contrasts. The Benjamini–Hochberg correction for multiple hypothesis testing was applied alongside a log-FC shrinkage using the apeglm normalisation method48. Differentially expressed genes were defined using an absolute log-FC threshold of 1 and an adjusted p-value of <0.05.

Gene set enrichment analysis

Gene set enrichment analysis (GSEA) using Gene Ontology (GO) and Kyoto Encyclopaedia of Genes and Genomes (KEGG) terms was performed using the ClusterProfiler library (version 4.10.0) in R, using the log-FC ranking of all genes in the study. Significant gene sets were defined using a p-value threshold of <0.05 and an absolute normalised enrichment score (NES) > 1. Redundancy in GO GSEA results was managed using the simplify function from the ClusterProfiler library using a similarity cutoff of 0.75. GSEA results were visualised using enrichplot (version 1.24.2).

Constraint-based modelling

Constraint-based modelling is a family of computational methods that formulate constraints as equations to define the feasible states of a metabolic system or flux space. A metabolic network can be represented using the stoichiometric matrix N of m × r, where m corresponds to the number of metabolites (M) and r the number of reactions (R). The fundamental constraints used to define the flux space are the mass balance constraint:

$$N\cdot \overrightarrow{v}\,=\,0$$
(3)

the thermodynamic constraints on irreversible reactions

$${v}_{i}\ge 0\forall i\in {\rm {Irrev}}$$
(4)

and the capacity constraints which limit the total flux through each reaction:

$${\alpha }_{i}\le {v}_{i}\le {\beta }_{i}$$
(5)

When applied to boundary reactions, the capacity constraints define the metabolites produced/consumed by the system49. By boundary reaction, we mean reactions representing sources/sinks that consume/produce a single metabolite. Boundary reactions are referred to as exchange reactions, and are defined over each metabolite present in the environment. Boundary reactions are used to define growth conditions as well as to set sources and sinks to internal metabolites that correspond to a known dead-end or gap metabolites50.

Flux balance analysis

Flux balance analysis (FBA) is a constraint-based approach for finding flux distributions that maximise the flux through the biomass reactions51. FBA is formulated as a linear programme using the mass balance constraint (3), the thermodynamic constraint (4) and the boundary constraint (5). The resulting linear optimisation problem of FBA is the following:

$$\begin{array}{lll}{\rm{Maximize}}:Z &=& {v}_{{\rm {biomass}}}\\&&{\rm{s}}.{\rm{t}}.\\&&{N}\cdot \overrightarrow{v}\,=\,0\\&&{\beta }_{i}\le {v}_{i}\le {\beta }_{i}\end{array}$$
(6)

Parsimonious flux balance analysis

Parsimonious flux balance analysis (pFBA) is a constraint-based approach for finding flux distributions that minimise the total flux, and it is usually applied to generate solutions without inconsistent thermodynamic loops52. To formulate pFBA, reversible reactions must be split into irreversible reactions in opposite directions to guarantee non-negative fluxes and set Z* which usually correspond to the optimal value found by FBA (see Eq. (6)). After converting the network into an irreversible pFBA is formulated as follows:

$$\begin{array}{lll}{\rm{Minimize}}:Z &=& \mathop{\sum}\limits _{i}{v}_{i}\\&&{\rm{s}}.{\rm{t}}.\\&&{N}\cdot \overrightarrow{v}\,=\,0\\&&{0}\le {v}_{i}\le {\beta }_{i}\\&&{{\boldsymbol{c}}}^{\top }{\boldsymbol{v}}={Z}^{* }\end{array}$$
(7)

Modelling metabolic tasks

A metabolic task usually corresponds to a pathway leading to the production of metabolite P from metabolite S. In general, producing a metabolite P from a precursor S usually requires cofactors such as ATP, NADH and/or NADPH as well as the balancing of protons, water, etc. More formally, a metabolic task t is defined as a set of input metabolites \({M}_{{\rm {in}}}^{t}\) and a set of output metabolites \({M}_{{\rm {out}}}^{t}\)17. To implement a metabolic task t, all the exchange reactions of the model are first set to zero, and then source and sink boundary reactions are added for the set of inputs and outputs, respectively. Then, each input metabolite i is associated with a source reaction \({b}_{i}^{in}\forall i\in {M}_{in}\), and each output metabolite j with a sink \({b}_{j}^{{\rm {out}}}\forall j\in {M}_{{\rm {out}}}\). Sources and sinks are then bound according to the definition of the task (see Table 3 for an example).

Table 3 Example of a metabolic task corresponding to ATP regeneration in aerobic conditions (glycolysis + krebs cycle)
Full size table

Finally, to calculate the flux distribution for the task t, parsimonious flux balance analysis (7) is applied to find the feasible solution that minimises the sum over the total fluxes. This solution is usually used as the flux distribution for a task, and it is used to infer the active or flux-carrying reactions on the pathways.

Mapping gene expression into reaction using gene–protein-reaction rules

Gene–protein-reaction (GPR) rules are a key component of genome-scale metabolic models, enabling the integration of gene expression data with reaction activity30. GPRs are represented as logical expressions that combine gene identifiers using the AND operator for protein complexes and the OR operator for isoenzymes. These rules allow mapping gene expression values or fold-changes to metabolic reactions. GPR evaluation is performed recursively by traversing the expression tree, where leaf nodes represent gene identifiers and internal nodes represent logical operators. Below is the pseudo-code for the EvaluateGPR function, which determines whether a reaction is active, given a specific set of expressed genes.

Algorithm 1

Evaluation of a GPR rule of a reaction using gene expression values

1: function EVALUATEGPR(expr, values_dict, or_func)

2: if expr is a GPR object then

3: return EVALUATEGPR(expr.body, values_dict, or_func)

4: else if expr is a gene name (Name) then

5: if expr.id not in values_dict then

6: return 0

7: else

8: return values_dict[expr.id]

9: end if

10: else if expr is a boolean operation (BoolOp) then

11: if expr.op is OR then

12: if or_func = “max” then

13: return \(\mathop{\max }\limits_{i}\) EVALUATEGPR(expr.values[i], values_dict, or_func)

14: else if or_func = “sum” then

15: return \(\sum _{i}\) EVALUATEGPR(expr.values[i], values_dict, or_func)

16: else

17: raise UnsupportedGPROperator

18: end if

19: else if expr.op is AND then

20: return \(\mathop{\min }\limits_{i}\) EVALUATEGPR(expr.values[i], values_dict, or_func)

21: else

22: raise TypeError(“unsupported operation”)

23: end if

24: else

25: return 0

26: end if

27: end function

This algorithm evaluates gene–protein-reaction (GPR) expressions based on the activity values of individual genes provided in a dictionary (values_dict). If the mapped gene values are continuous (e.g. gene expression or log-fold change values), the AND and OR operators are replaced by MIN and MAX/SUM, respectively. For the application of the mapping for the TIDE algorithm, we used the absolute maximum instead of the maximum since log-fold changes can have negative values, as described and the original paper35.

In-silico gene knock-outs

In-silico gene knock-outs simulate the deletion of genes by constraining the associated reactions in a genome-scale metabolic model. Since genes are mapped to reactions via GPR associations, a gene deletion translates into setting the flux of all reactions catalysed exclusively by the corresponding gene product(s) to zero. In the context of FBA, this is implemented by modifying the flux bounds of the affected reactions: for each reaction i associated with the knocked-out gene, we set αi = βi = 0, effectively removing the reaction from the feasible flux space. The modified model is then solved using FBA (6) to determine how the gene deletion affects the optimal objective value, i.e. the biomass production. A significant reduction or complete loss of biomass flux indicates that the deleted gene is essential under the given environmental conditions. This approach allows for the systematic prediction of gene essentiality and the identification of potential drug targets or synthetic lethal gene pairs in silico. To predict the set of essential genes of a metabolic task, we just tested for the feasibility of the problem after inactivating the reaction related to the gene being knocked; if the problem is infeasible, the tested gene is defined as essential for the task.

Flux variability analysis

Flux variability analysis (FVA) was used to identify the minimum and maximum flux values each reaction can carry while satisfying the constraints of the FBA problem (Eq. (6)). For each reaction in the model, FVA solves two linear programmes, one minimising and one maximising the flux, under the same conditions53. We applied FVA individually for each metabolic task to assess the flexibility of the network in supporting specific functions.

Tasks inferred from differential expression

To investigate changes in metabolic pathway activity, we applied the tasks inferred from differential expression (TIDE) algorithm35. We used the manually curated list of 187 metabolic tasks and their reference flux distributions. Log-fold change (log-FC) values from differential gene expression analysis were mapped onto the flux-carrying reactions associated with each task via their gene–protein-reaction (GPR) rules. In this mapping, each gene was substituted with its corresponding log-FC value. GPR rules were evaluated by interpreting logical AND and OR operators as the min and absmax functions, respectively, and resolving the resulting expression recursively. Genes with non-significant adjusted p-values were masked by setting their log-FC values to zero before evaluation. The statistical significance of the resulting task scores was assessed through 10,000 permutations. A task was considered significantly altered if its associated p-value was below 0.025, reflecting a two-sided testing strategy.

TIDE essential genes

To extend and complement the original TIDE framework, we developed an approach focused on the identification of essential genes required for the execution of curated metabolic tasks. For each task t, we performed an in silico gene knockout screening across all genes in the metabolic model. Specifically, for each gene g, the procedure consisted of the following steps: (1) identifying the set of reactions deactivated by the knockout of g; (2) constraining the flux of these reactions to zero; and (3) computing the flux distribution for task t using parsimonious flux balance analysis (see Eq. (7)). If the optimisation problem became infeasible, gene g was classified as essential for task t. This procedure was repeated for all genes and tasks, resulting in a gene-task matrix representing the essential genes for each metabolic task. The metabolic score of a task t was computed as the average log-fold change (log-FC) of the essential genes associated with that task. As in the original TIDE framework, log-FC values with non-significant adjusted p-values were masked to zero before evaluation, and statistical significance was assessed using 10,000 permutations. A two-sided testing approach was applied, with a significance threshold of p < 0.025.

Genome scale-metabolic model

We retrieved the genome-scale metabolic model Human-GEM version 1.18 from the official repository (https://github.com/SysBioChalmers/Human-GEM). The model accounts for 2897 genes, 11,364 metabolic reactions, 1721 exchange fluxes, and 8499 metabolites and is the most comprehensive description of human metabolism19. We used the list of selected metabolic tasks previously published by Richelle et al. 202136, which includes 195 metabolic tasks associated with 7 metabolic systems (energy, nucleotide, carbohydrate, amino acid, lipid, vitamin & cofactor, and glycan metabolism). Although this list of tasks was defined for the Recon 2.2 model18, the Human-GEM repository already includes a translated version of these metabolic tasks. A preliminary analysis showed that 9 tasks were inconsistently defined due to incorrect mapping of metabolite identifiers between metabolic Recon2.2 and the Human-GEM. Additionally, we identified 18 tasks that resulted in infeasible problems due to issues with the bounds of the inputs and/or outputs. Inconsistent tasks were manually curated by correcting metabolite identifiers. To curate infeasible tasks, we manually adjusted upper and lower bounds for the input and/or output metabolites, or by updating the compartments of some metabolites. After the curation process, 19 metabolic tasks were reconciled to the Human-GEM model, whereas 8 tasks remained either inconsistent (1) or infeasible (7). A summary of the curation processes and the curated list of tasks are provided in Supplementary Data 2.

Computational tools

All statistical analyses were conducted using R (version 4.4.1). Figures were generated using the following R libraries: tidyplots (version 0.1.2), ggcorrplot (version 0.1.4.1), ggVennDiagram (version 1.5.2), and pheatmap (version 1.0.12). TIDE and TIDE-essential algorithms were implemented in an open-source Python package and command-line tool, MTEApy, built on top of the COBRAPY54 library. The source code is available at: https://github.com/bsc-life/mteapy.