Digital twins for in vivo metabolic flux estimations in patients with brain cancer

Summary

Recent advancements in metabolic flux estimations in vivo are limited to preclinical models, primarily due to challenges in tissue sampling, tumor microenvironment heterogeneity, and non-steady state conditions. To address these limitations and enable flux estimation in human patients, we developed two machine learning-based frameworks. First, the digital twin framework integrates first-principles stoichiometric and isotopic simulations with convolutional neural networks to estimate fluxes in patient bulk samples. Second, the ¹³C-scMFA framework combines patient scRNA-seq data with ¹³C-isotope tracing, allowing single-cell-level flux quantification. These studies allow quantification of metabolic activity in neoplastic glioma cells, revealing frequently elevated purine synthesis and serine uptake compared to non-malignant cells. Our models also identify metabolic heterogeneity among patients and mice with brain cancer, in turn predicting treatment responses to metabolic inhibitors. Our frameworks advance in vivo metabolic flux analysis, may lead to novel metabolic therapies, and identify biomarkers for metabolism-directed therapies in patients.

Graphical Abstract

eTOC

Quantifying metabolic activity in patient tumors could advance personalized cancer targeting. Meghdadi et al. develop a digital twin framework using machine learning to quantify metabolic fluxes in tissues from patients with glioma, identifying which patients may benefit from different targeted metabolic therapies like specialized diets or pharmacologic agents.

Introduction

Cancer therapies work best when the pathways they target are active in a tumor. Despite development of numerous metabolism-targeted therapies over past decades^1,2, oncologists cannot quantify the activity of metabolic pathways in patient tumors. Stable isotope tracing³ and metabolic flux analysis (MFA) can quantify activity in vitro but are challenging to apply in vivo. In stable isotope tracing, labeled nutrients are introduced into a biologic system, and active metabolic pathways transfer their labeled atoms to downstream metabolites, rendering them heavier than their expected molecular weights. These weight shifts are detectable by methods like mass spectrometry. Label extents and patterns in downstream metabolites provide information about the consumption of labeled nutrients⁴ but cannot quantify rates of activity. Quantification of metabolic fluxes can be determined using advanced frameworks such as MFA, which requires additional conditions and data such as isotopic steady state and measurement of nutrient uptake and secretion^5,6.

Since surgical tumor resection is often standard of care in cancer patients, administering isotopically labeled nutrients and sampling metabolites from the resected tissue is practical and has been performed in different settings^7–9. The practicalities of stable isotope infusions during clinical tumor resections typically necessitate (1) non-steady state conditions due to limited tracer infusion times and (2) single timepoint measurements because sample acquisition is typically only done once⁹. Hence, traditional MFA techniques cannot be used to measure metabolic fluxes as they require single timepoint steady state enrichment profiles or multiple-timepoint isotope enrichment data under isotopic nonsteady state conditions.

Digital twins have been implemented for various healthcare applications by mimicking real-world physical entities^10–13, yet their application in cancer metabolism is missing. This study is the first to overcome challenges of quantifying metabolic fluxes in patient tissues by implementing a digital twin framework that integrates isotopic nonsteady state metabolic flux analysis (INST-MFA) for in vivo data and convolutional neural network (CNN) to define metabolic pathway activity in human tumors. Digital twins allow identification of structure and complex patterns underlying in vivo isotopic tracing data, thereby identifying patients most likely to respond to different metabolic therapies. Another limitation of isotope tracing data is that standard metabolomic techniques require tissue homogenization; however, tumors are comprised of heterogeneous neoplastic and non-neoplastic cells, each with their own metabolic signature. Understanding the metabolic contribution of each cell population in the tumor microenvironment (TME) is not achievable by isotope tracing. To address this issue and introduce mechanistic insights at a single-cell level, we developed ¹³C-scMFA, an integrated single-cell flux estimation analysis (scFEA) and MFA framework that identifies metabolic fluxes within the TME. Our ¹³C-scMFA approach pairs single-cell RNA sequencing with ¹³C-metabolic tracing data to estimate single-cell fluxes (scfluxes).

We validated our digital twin approach on two clinically relevant metabolic pathways: serine metabolism and purine metabolism. Our prior study found that glioblastoma (GBM) tumors consume high environmental serine relative to surrounding cortex, while tumor growth in mice could be impeded by serine/glycine-deficient (-SG) diets⁹. Hence, we used our digital twin framework to understand contributions of glucose-derived (de novo) serine synthesis, plasma serine uptake, and TME-derived serine uptake in patients with glioma. Identification of tumor dependency on serine sources might allow us to determine which patients may benefit from a -SG diet. Our prior investigations also found that GBMs preferentially divert glucose towards nucleotide biosynthesis⁹ to support treatment resistance¹⁴. Here, we used our digital twin approach to resolve between inosine monophosphate dehydrogenase (IMPDH)-dependent de novo synthesis and hypoxanthine-guanine phosphoribosyl transferase (HPRT1)-dependent salvage pathways as dominant routes for guanosine monophosphate (GMP) synthesis in patients with glioma. Quantifying tumor reliance on GMP sources could inform which patients may benefit from mycophenolate mofetil (MMF), an FDA-approved drug targeting IMPDH. To validate our model experimentally, we compared predicted metabolic fluxes to [U¹³C]-glucose-infused mice to estimate treatment responses for (1) dietary serine/glycine restriction and (2) pharmacologic IMPDH inhibition with MMF. To further validate our model computationally and investigate metabolic crosstalk in the TME, we used matched scRNA-seq and ¹³C-metabolic isotope enrichment data from patients’ gliomas and non-malignant cells in the cortex and quantified metabolic fluxes of various cell populations using ¹³C-scMFA. Notably, we have shown that our models can identify patients who may benefit from MMF or -SG diets, potentially enabling effective personalized metabolic treatments for patients with gliomas. In summary, our digital twin approach (1) quantifies metabolic activities in human tumors using single-timepoint data, (2) can assess target-engagement of metabolic therapies, and (3) may provide biomarkers for clinical application of nucleotide- and serine-directed therapies in brain cancer patients.

Results

A digital twin framework quantifies in vivo metabolic fluxes in patients with glioma

We introduce a digital twin approach that leverages scRNA-seq and in vivo ¹³C-enrichment data from patients with brain cancer⁹ (Figure 1A) and employs flux balance analysis (FBA) and INST-MFA to generate thousands of patient fluxes and nearly one million time-dependent isotopologue profiles (Figure 1B). To ensure our simulated MIDs can capture the variability seen in clinical scenarios, the user-defined simulation parameters including flux bounds and input metabolite MIDs are chosen such that simulated MIDs represent physiologically relevant ranges of MIDs in patient tumors (Figure S1). Simulated MIDs and fluxes serve as digital twins of patients and feed into a CNN (Figure 1B). CNN predicts contributions of various sources of a metabolite given a set of MIDs at a specific timepoint.

Figure 1 – Digital twin framework to predict relative metabolic fluxes in patient tumors.

(A) Data used in digital twin framework. Metabolite labeling data from tissues and plasma from patients infused with [U¹³C]-glucose were analyzed; in parallel, metabolic gene expressions across cell types were investigated by scRNA sequencing. (B) Digital twin framework consists of simulation of stoichiometry-balanced fluxes, and MIDs based on prior knowledge of patient ¹³C-enrichments, and convolutional neural networks predicting relative fluxes in patient tumors (metabolic CNN). Validation methods include experiments using mice receiving targeted therapy and single-cell metabolic flux analysis (¹³C-scMFA) – a new method proposed here that integrates metabolic gene expression and bulk ¹³C-MIDs to estimate single-cell fluxes. Our framework may predict response to metabolic-targeted therapies in patients with glioma.

CNN model validity can be tested experimentally in laboratory models such as patient-derived xenografts (PDXs). CNNs can predict the dominant sources of a given metabolite across a variety of PDXs. The PDX models predicted to have a higher reliance on a given source should have the greatest reduction in tumor growth or viability when that source is experimentally inhibited. The CNN-predicted relative metabolic fluxes can also be validated if they are correlated with an independent flux estimation tool. Here, we leverage combined [U¹³C]-glucose isotope tracing and scRNA-seq data from patients with glioma and develop an integrative scFEA and MFA approach (¹³C-scMFA). An integrated analysis of this nature allows for an independent and robust validation of the CNN model by comparing CNN-predicted relative fluxes with scflux estimates derived from ¹³C-scMFA. If there is a strong correlation between the two sets of flux estimates, it would further substantiate the predictive power of the CNN model in capturing the true metabolic behavior of glioma cells. Additionally, ¹³C-scMFA can aid resolving metabolic heterogeneity across cell types and allow estimation of metabolic interactions within the TME (Figure S1).

Single-cell flux balance analysis identifies TME-derived serine as a source for GBM-neoplastic cells

Our previous study found that gliomas often rely on exogenous serine⁹. This exogenous serine could be derived from non-malignant cells in the microenvironment or from the bloodstream. This distinction has therapeutic implications, as strategies to lower circulating serine—now undergoing clinical investigation—may not target TME-derived serine. To understand which TME cell types might secrete serine for glioma cells, we performed a metabolic interaction analysis on scRNA-seq data generated by Darmanis et al.¹⁵, which included different cell types of GBM and its periphery (Figure S2A–B). MEBOCOST¹⁶ was used to infer a metabolite communication score between a sender cell type, which has a high metabolite presence inferred by gene expression, and a receiver cell type, which has high expression of metabolite transporters. Considering all metabolic communications, astrocytes had the highest score for metabolite secretion, and neurons had the highest score for metabolite uptake (Figure S2C–D). Cell type connectivity related to serine transport had the highest frequency compared to other metabolites (Figure S2E). Further, the expression of genes related to serine production and consumption infers serine abundance which is the highest/lowest in astrocytes/neurons and suggests that astrocytes are potential candidates for serine secretion into the TME (Figure 2A, S2F). Consistent with the astrocyte/neuron serine shuttle¹⁷, this analysis shows the highest serine communication score for astrocyte/neuron interactions, suggesting astrocytic serine secretion and neuronal serine uptake (Figure 2B, S2G). This analysis also suggests that neoplastic cells may acquire serine using SLC38A2 and SLC6A9 (Figure S2H). However, it was unclear how much TME-derived serine could be taken up by neoplastic cells.

Figure 2 – Investigation of TME metabolic interactions.

(A) Metabolite accumulation score (MAS) is defined as sum of expression of genes producing serine de novo subtracted by those consuming serine. (B) Network plot of MEBOCOST analysis showing a high overall communication score for serine between astrocyte and neurons. Overall communication score represents the sum of −log10(FDR) of all metabolite-sensor communications between sender and receiver cell types. Arrows indicate communications from a sender cell type to a receiver cell type. (C) Modified single-cell flux estimation analysis (modified scFEA) framework includes enzymes producing, consuming, and transporting serine in each cell. Single-cell fluxes are generated based on gene expression balanced by stoichiometry for each cell. The exchange fluxes are balanced in TME. (D-G) Distribution of fluxes in three-compartmental model described in C: (D) glucose-derived serine synthesis, (E) serine consumption excluding glycine formation, (F) serine uptake/secretion, (G) serine-derived glycine formation. Stats represent Wilcoxon rank-sum test p-values (#: p<2.22e-16). (H) Experimental validation for serine de novo synthesis and serine secretion/uptake (J-K). (I) Serine M+3 abundance after 3h in media (normalized to cell protein) from [U¹³C]-glucose tracing in primary mouse astrocytes and neurons, and patient-derived GBM38 cells. (J-K) [U¹³C]-serine tracing in astrocytes, neurons, and GBM38 cells. (J) Serine M+3 consumption from media after 5 min was calculated by subtracting unconditioned media values. (K) Intracellular serine M+3 levels after 5 min. (n=4 biological replicates per group). Stats show p-values from unpaired two-sided t-tests with Welch’s correction.

To address this question, we predicted fluxes of serine production, consumption, and uptake/secretion in astrocytes, neurons, and neoplastic cells using a similar approach as scFEA¹⁸ (Figure 2C, S2I). In scFEA, intracellular fluxes are balanced for each cell. We extended the scope of scFEA by incorporating intercellular fluxes and ensured their balance within the TME (Figure 2C, S2J). This analysis estimated that astrocytes have greater de novo serine synthesis (Figure 2D) and lower serine consumption flux than neurons and neoplastic cells (Figure 2E). Hence, the remaining synthesized serine is likely secreted into the TME (Figure 2F). Neoplastic cells acquire more serine from the TME than neurons since they have the highest serine consumption (Figure 2E–G). Our results also estimated that neoplastic cells have higher serine-derived glycine formation (Figure 2G), which could drive the folate cycle and de novo purine biosynthesis.

We additionally validated scFEA results by measuring extracellular glucose-derived serine in primary brain cells and GBM38 explants in vitro (Figure 2H). When cells were fed [U¹³C]-glucose tracer, serine M+3 in astrocyte media confirmed astrocytic serine synthesis and secretion (Figure 2I). In contrast, higher neuronal and GBM uptake of extracellular media serine M+3 compared to astrocytes was observed (Figure 2J). Consistent with media measurements, intracellular serine M+3 abundance increased in neurons and GBM38 cells (Figure 2K), further indicating that neurons and GBM38 cells exhibit net serine uptake while astrocytes exhibit net secretion. In summary, these results suggest that astrocytes synthesize and secrete serine, which is consumed both by neurons and glioma cells.

Digital twin framework predicts relative fluxes of serine sources in human glioma and cortex using [U¹³C]-glucose labeling

Relying solely on scRNA-seq data lacks discriminatory power required to differentiate between the two primary sources of exogenous serine (TME and bloodstream), as serine transporter genes are associated with both sources and gene expression does not necessarily imply metabolic activity. However, stable isotope tracing examines metabolic activity directly. Previously, we traced [U¹³C]-glucose in 8 patients to determine glucose carbon fates in gliomas vs. adjacent cortex via mass spectrometry⁹ and applied ¹³C-enrichment data in models here. Our cohort comprised 6 patients with GBM, 1 patient with IDH-mutant anaplastic oligodendroglioma (P4), and 1 patient with IDH-wildtype diffuse hemispheric grade 4 glioma (P6); samples comprised contrast-enhancing (E, 7/8 patients) and non-enhancing (N, 8/8 patients) glioma regions and adjacent cortex (C, 8/8 patients).

During [U¹³C]-glucose tracer infusions, multiple serine acquisition routes are labeled, which may result in similar isotopologue patterns that make distinguishing between contributions of these routes challenging (Figure 3A). For example, we observed that plasma ¹³C-serine contains one carbon label (M+1), possibly originating from liver or kidney reverse serine hydroxymethyltransferase (SHMT) flux (Figure S3A); while phosphoglycerate contains predominantly M+3 labeling (Figure S3B). However, two other potential sources of GBM serine are the TME-derived serine that includes M+1-M+3 isotopologues (Figure S3C) and SHMT flux that combines glycine (Figure S3D) with one labeled carbon 5,10-methylene tetrahydrofolate (MTHF). In summary, serine M+3 may be obtained from phosphoglycerate M+3 and/or TME-derived serine M+3, while serine M+1 may be obtained from plasma serine M+1, SHMT flux with labeled MTHF, and/or TME-derived serine M+1 (Figure 3A). These collective possibilities of labeled carbon combinations complicate the distinction of GBM serine sources.

Figure 3 – Metabolic CNN predictions of relative fluxes of serine sources.

(A) Routes of serine in glioma tissue and their isotopic contributions. (B) Serine metabolic model used to simulate fluxes and MIDs. (C) Design of a convolutional neural network (CNN) that can predict de novo serine synthesis, plasma serine uptake, and TME-derived serine uptake fluxes for a set of MIDs. (D) Evaluation of CNN model on test simulated data. (E) Predicted relative flux of serine source in tissues from GBM12-, GBM38-, and HF2303-bearing mice (n=100 samples from a normal distribution with mean and standard deviation of 3–7 biological replicates per group). (F) Validation of serine digital twins in mice fed control or serine/glycine-restricted diets (-SG) via [U¹³C]-glucose infusions. (G) Predicted relative flux of plasma serine uptake in control and -SG. Stats represent p-value of Wilcoxon rank-sum test corrected by Holm–Bonferroni method (* p<0.05, ** p<0.01, *** p<0.001, **** p<0.0001). (H) Prediction of relative fluxes of serine sources in patients (C: cortex, N: non-enhancing tumor, E: enhancing tumor) using MIDs (n=100 samples from a normal distribution with mean and standard deviation of 1–3 technical replicates per patient sample). (I) Correlation between ratio of experimental MIDs and CNN-predicted fluxes. Stats represent p-value of Pearson’s r correlation. (J) Serine MFA model informed by CNN-predicted relative fluxes. (K-L) Comparison of glucose-derived serine synthesis flux (K) and plasma serine uptake (L) between cortex and glioma estimated by MFA model described in (J). (SERg: glioma serine, PGg: glioma phosphoglycerate, SERp: plasma serine, SERc: cortex serine, PGc: cortex phosphoglycerate).

To comprehensively account for all labeled serine sources and unlabeled serine derived from autophagy and protein degradation, we developed a flux and MID simulation framework (Figure 3B). Given flux bounds, stoichiometry, range of input metabolite MIDs, and concentration of balanced metabolites, flux sets (Figure S3E) with nearly 1 million time-dependent MID profiles were simulated which closely resemble MIDs observed in patient specimens (Figures S3F–G). Simulated MIDs were used to train a CNN model to predict relative fluxes of serine sources in glioma and cortex (Figure 3C). CNN performance was evaluated during training (Figure S3H), and serine sources predictions in glioma and cortex tightly correlated with the relative fluxes derived from the test simulated data (Figure 3D).

The trained CNN was then used to predict contributions of serine sources in GBM12, GBM38, and HF2303 tumor-bearing mice infused with [U¹³C]-glucose, previously⁹. Our model predicted higher de novo serine contributions in the cortex but higher exogenous serine dependence in all tumor types, with HF2303 and GBM38 tumors exhibiting greater plasma serine uptake than GBM12 (Figure 3E). These predictions of higher uptake in GBM than cortex were confirmed via direct [U¹³C]-serine tracing experiments showing higher accumulation of exogenous plasma serine tracer into tumors than cortex⁹. To validate these predictions, we infused [U¹³C]-glucose into these mouse models fed control or -SG diets⁹ (Figure 3F, S3I–K). Our model predicted that -SG diet lowers plasma serine uptake flux in all tumors, with more pronounced decreases in GBM38 and HF2303 (Figure 3G). These latter two models are more sensitive to -SG diets in tumor burden studies⁹.

We then applied the trained CNN model to patients’ MIDs (Figure S3A–C) to predict relative fluxes of serine sources in glioma and cortex. Glucose-derived serine synthesis was the major source of serine in cortex for all patients (Figure 3H), while dominant serine sources in gliomas varied. For example, tumor P4N/E predominantly acquired serine from plasma while tumor P1N/E acquired most of its serine from the TME. This suggests that P4 might respond to dietary serine depletion, but P1 may require broader serine transport inhibition. Intuitively, since M+3 patterns come from phosphoglycerate in glioma and cortex, we anticipated a correlation between glucose-derived serine flux and ratios of serine M+3/phosphoglycerate M+3 (Figure 3A). Additionally, as expected plasma serine uptake flux correlated with serine M+1/plasma serine M+1 (Figure 3I). Although TME-derived serine uptake flux added some complexity to glioma serine patterns, a high correlation was still observed between these relative fluxes and patient MID ratios (Figure 3I, S3L–M), substantiating clinical relevance of CNN-based metabolic flux estimation.

Since the CNN model predicts fluxes relatively in each tissue, we used MFA informed by CNN predictions to compare flux between cortex and glioma (Figure 3J). MFA alone cannot estimate fluxes because this system is underdetermined, but with the help of CNN, the uncertainty of MFA model decreases. MFA-estimated glucose-derived serine synthesis flux was higher in cortex than glioma for all patients (Figure 3K), while plasma serine uptake flux varied (Figure 3L). These results suggest that patients with higher plasma serine uptake in glioma than cortex (e.g., P4, P6) may respond more favorably to dietary serine depletion.

Digital twin framework predicts relative fluxes of GMP sources in patient gliomas

Recently, we observed widespread higher ¹³C-purine labeling from [U¹³C]-glucose in gliomas than cortex in mice and humans⁹. Among these purines, GMP was the only metabolite with consistently higher enrichment across all patient gliomas relative to cortex. This suggested a significant role for GMP production in metabolic reprogramming associated with gliomagenesis^19–21. GMP enrichment in glioma tissues indicates enhanced purine de novo synthesis or salvage pathways, pivotal for nucleic acid synthesis and thus rapid proliferation of cancer cells. Understanding the dominant pathway of GMP synthesis might predict which patients could respond to IMPDH inhibitors in our clinical trial (NCT04477200). Hence, we applied our digital twin framework to quantify de novo (IMPDH-dependent) and salvage (HPRT1-dependent) GMP synthesis pathways.

A simple scenario for distinguishing between de novo and salvage pathways based on MIDs is that salvage synthesis contributes M+5 purines if labeled ribose 5-phosphate (R5P) contains only the M+5 isotopologue; whereas de novo synthesis produces M+9 purines (R5P + glycine + 2 MTHF + CO₂) if serine contains only M+3 resulting in glycine M+2 and MTHF M+1 (Figure 4A) as observed in vitro²². However, due to limited infusion times, slow purine metabolism rates, isotopic pattern complexity, and tumor heterogeneity, the enrichment of purine M+6-M+9 was low (Figure S4A–B), impeding distinctions between these pathways without further modeling. We observed that R5P enrichment includes M+1 to M+5 isotopologues derived from complex isotopic turns in pentose phosphate pathway (Figure 4B, S4C). Due to the broad range of R5P and serine isotopologues in vivo, multiple purine isotopomers can be generated de novo with the same numbers of labeled carbons as in the salvage pathway (Figure 4C). Incorporation of unlabeled substrates in de novo purine synthesis predominantly results in M+1 to M+5 purine isotopologues (Figure 4C); thus, the probability of generating M+1 to M+5 is greater than M+6 to M+9 (Figure S4A–B). Therefore, the inability to detect M+6 to M+9 isotopologues does not imply that de novo synthesis is inactive.

Figure 4 – Prediction of relative fluxes of GMP sources.

(A) Generation of IMP M+9. (B) Isotope tracing in pentose phosphate pathway to generate M0-M5 R5P. (C) Production of isotopomers of nucleotides through de novo IMP synthesis. The last isotopomer in each column can be also produced through salvage of unlabeled nucleobases. (D) Purine metabolic model used to simulate fluxes and MIDs. (E) Design of a convolutional neural network (CNN) that can predict IMPDH-dependent GMP synthesis flux to total GMP synthesis flux (salvage and de novo GMP synthesis) for a set of MIDs. (F) Evaluation of CNN model on test simulated data. (G) Schematic of mycophenolate mofetil (MMF) treatment experiment with GBM38-bearing mice. (H) Sources of GMP synthesis (salvage and de novo). (I) CNN prediction of relative IMPDH-dependent GMP flux in GBM PDXs (Ctrl) and treated with MMF at 150 mg/kg (low) concentration with 1, 2, and 4 doses and 1 dose of 300 mg/kg (high) concentration. Different colors represent different mice (n=100 samples with imputation (dots with the same color) from a normal distribution with mean and standard deviation of 3 technical replicates). Black squares represent means of biological replicates for each condition. Stats represent Wilcoxon rank-sum test p-values (#: p<2.22e-16), one-way ANOVA with Benjamini and Hochberg correction (FDR=0.001) resulted in p<0.0001 for each treatment compared to control. (J-L) ¹⁵N-amide-glutamine infusion in intracranial GBM38-bearing mice. (J) Schematic of purine isotopologues produced from ¹⁵N-amide-glutamine. Mean enrichment (%) of (K) Inosine and (L) GTP normalized to glutamine mean enrichment. (n=4 technical replicates from 3–4 biological replicates) (M) Tracing with [U¹³C]-glucose and [U¹³C]-serine in control and MMF-treated GBM38-bearing mice. (N) Fractional contribution of de novo and salvage GMP synthesis estimated by a linear regression model (n=3–4 biological replicates). (O) CNN-predicted relative de novo GMP synthesis flux in TRP and GBM38 models. (P) CNN prediction of relative IMPDH-dependent GMP flux in patients given imputed patient MIDs (n=100 samples from a normal distribution with mean and standard deviation of 1–3 technical replicates per patient sample). Stats in K-L,N show p-values from unpaired two-sided t-test with Welch’s correction and in O represents Mann-Whitney test (* p<0.05, ** p<0.01, *** p<0.001, **** p<0.0001).

Our digital twin framework addresses complexity of these patterns and closely resembles patient MIDs (Figure S4D–F). Since cortical GMP enrichment is <1% in all patients (Figure S4B) – indicating low purine synthesis – and labeling of exchange nucleotides is directly incorporated into the tissue metabolites through uptake and secretion, our purine model is simpler than the serine model in terms of including reactions only for glioma (Figure 4D). The CNN model was trained on the simulated MIDs to predict the relative contributions of IMPDH-dependent and HPRT1-dependent GMP synthesis in patient gliomas (Figure 4E). The learning curve shown in Figure S4G demonstrates a lack of overfitting, and predictions for the test dataset closely correlate with the simulated fluxes (Figure 4F).

To validate purine digital twins, GBM38-bearing mice were treated with MMF and infused with [U¹³C]-glucose (Figure 4G), confirming whether the CNN model predicted decreased IMPDH-dependent flux after MMF treatment (Figure 4H). Measured ¹³C-MIDs were fed to the CNN to predict de novo GMP synthesis contribution (Figure 4I, S4H). While control GBM generated its GMP predominantly through IMPDH, this activity was reduced in mice treated MMF. Increased inhibition of IMPDH-dependent GMP synthesis was observed with higher and/or more frequent MMF doses (Figure 4I). Further, lower GMP/IMP abundance ratios in treated groups compared to control groups indicated pharmacological target engagement with IMPDH (Figure S4I). We also used orthogonal ¹⁵N-amide-glutamine tracing to confirm that MMF reduces contribution of de novo GMP synthesis (Figure 4J). MMF treatment caused accumulation of IMPDH-upstream metabolites (Figure 4K, S4J) and dissipation of IMPDH-downstream metabolites (Figure 4L, S4K). To test the model’s ability to deconvolute even more complex MIDs, we generated datasets in which GBM38-bearing mice were labeled with combined [U¹³C]-glucose and [U¹³C]-serine tracers after MMF treatment (Figure 4M). Although distinction between de novo and salvage pathways is not feasible from the isotope tracing data itself because salvage metabolites such as guanine and guanosine are also labeled (Figure S4L), a linear regression analysis²³ suggested lower de novo synthesis contribution in the MMF-treated group (Figure 4N). We further tested [U¹³C]-glucose labeling in TRP tumors^24,25 (Figure S4M), which are less sensitive to MMF than GBM38²⁶. Consistent with greater GBM38 MMF sensitivity, our model predicted higher IMPDH-dependent GMP synthesis (Figure 4O). In summary, our CNN framework accurately predicted a reduction in IMPDH-dependent flux when an IMPDH inhibitor was administered or a more resistant model used, thereby validating our model experimentally.

We then applied the trained CNN model to patients’ MIDs (Figure S4A–C) to predict contribution of IMPDH-dependent GMP synthesis to total GMP synthesis in these gliomas (Figure 4P). In all patients’ tumors analyzed, at least a third of GMP was synthesized through IMPDH (P5E), while some tumors (P2 and P6) were almost entirely dependent on IMDPH-driven GMP synthesis.

Integrating scRNA-seq and ¹³C-tracing delineates TME metabolic heterogeneity

Considering availability of patient ¹³C-isotope tracing data, our CNN framework enabled prediction of relative fluxes in bulk tissues. However, the metabolic activity of TME cells can vary, and metabolic crosstalk between different cell types in the TME can promote tumor growth²⁷. To enhance estimations by incorporating metabolic fluxes across TME cell types, 12 samples of scRNA-seq data from 6 patients (Figure 5A) were combined with bulk ¹³C-isotope tracing data.

Figure 5 – Single-cell flux quantification of serine metabolism with ¹³C-scMFA.

(A) UMAP projection of 126,507 cells from 12 samples of 6 patients with glioma. (B) UMAP projection showing Louvain clusters. (C) Butterfly plot of neoplastic cells per Neftel et al.’s neoplastic subtypes. Each quadrant represents a phenotype: mesenchymal-like (MES-like), neural progenitor-like (NPC-like), oligodendrocyte progenitor-like (OPC-like), astrocyte-like (AC-like). Colors represent Louvain’s clusters. (D) Heatmap of top 20 differentially expressed genes in clusters ranked by average log2 fold change. (E) UMAP colored by cell types. (F) Dot plot of cell type-specific marker genes. (G) Fraction of cells in patient samples colored by cell types and number of cells in each patient sample. (H) Molecular subtype classification in patients’ neoplastic cells and all cell types. Colors show scaled AUCell score for each program. (I) ¹³C-scMFA serine model for single cells. (J) Distribution of scfluxes in neoplastic cells for serine sources including glucose-derived serine synthesis, plasma serine uptake, TME-derived serine uptake in patients. (K) Correlation between average neoplastic scfluxes of serine sources (normalized to sum of patients’ average scfluxes) and CNN-predicted fluxes. R and p represent Pearson’s r correlation and p-value. (L) Distribution of single-cell fluxes of serine-derived glycine formation divided by total serine consumption in astrocytes, neurons, and neoplastic cells. Stats in (J) and (L) represent p-value of Wilcoxon rank-sum test corrected by Holm–Bonferroni method (* p<0.05, ** p<0.01, *** p<0.001, **** p<0.0001).

To elucidate cellular heterogeneity in patient gliomas, 16 clusters were identified based on distinctive gene expression (Figure 5B). Cells were identified as malignant or non-malignant by combining level-1 of GBmap marker gene expression²⁸ (Figure S5A) and copy number alterations using CopyKAT²⁹ (Figure S5B). Further, neoplastic cells were classified by their cell states including AC-, OPC-, MES-, and NPC-like³⁰ (Figure 5C). Non-neoplastic cells were classified by their marker gene expression (Figure 5D–F). Differential expression analysis identified a proliferative neoplastic cell type (cluster 8; Figure 5D) which also expressed cell cycle genes³⁰ (Figure S5C). As expected from previous analyses²⁸, the two major cell types were neoplastic (68.9%) and myeloid cells (25.51%) (Figure S5D).

In samples from patients with GBM, neoplastic cells were mainly observed in differentiated states (AC-like/MES-like), while stem-like states (OPC-like/NPC-like) were more common in other patients (Figure 5G). This pattern aligns with molecular subtype classifications, where differentiated cells express mesenchymal/classical programs and stem-like cells exhibit proneural program (Figure 5H). Further, the mesenchymal program is associated with myeloid recruitment as previously reported³¹ (Figure 5G–H). In summary, this analysis elucidates heterogeneity of TME and patient-specific molecular characteristics.

To investigate cellular metabolic variations and metabolic crosstalk in patients, we implemented an integrated scFEA and MFA approach (¹³C-scMFA) using scRNA-seq and bulk ¹³C-MIDs to quantify intra- and intercellular fluxes. In ¹³C-scMFA, we curated a metabolic model for intracellular and exchange fluxes based on analyses shown in Figure 2. scfluxes are generated based on the expression of genes associated with each reaction through a neural network¹⁸. Bulk ¹³C-MIDs of tumor or cortex samples are assigned to each cell based on their tissue of origin. Finally, scfluxes are optimized such that accumulation of cellular and exchange metabolites, and accumulation of MIDs in tissues are minimized (Figure S5E). Since gene expression might not correlate with metabolic activity of the cell (Figure S5F), our model uses ¹³C-MIDs to estimate scfluxes instead of inferring metabolic activity by gene expression alone.

A critical aspect of tumor metabolism influencing disease progression and therapeutic response is the metabolic crosstalk within the TME, which can be resolved from plasma metabolites when their isotopologue patterns are different although transporter genes are common between them. One example of ¹³C-scMFA application is serine metabolism in which associated genes for TME-derived serine and plasma serine are the same, but ¹³C-scMFA estimated distinct fluxes for these two sources because plasma serine labeling contains M+1 and TME-derived serine contains M+1-M+3 (Figure 5I–J, S3C). In addition to exogenous fluxes, ¹³C-scMFA incorporates glucose-derived serine synthesis and serine consumption routes in astrocytes, neurons, and neoplastic cells (chosen based on Figure 2) where the former two reside in cortex and the latter in glioma.

Our results suggest that astrocytes exhibit higher glucose-derived serine flux while neurons exhibit higher TME-derived serine uptake flux across patients (Figure S5G). On the other hand, scfluxes of neoplastic cells represent various contributions of serine sources across patients (Figure 5J) highly correlated with CNN relative fluxes (Figure 5K). Collectively, both ¹³C-scMFA and CNN methods agree on the dominant source of serine in patients and suggest who may benefit from a serine/glycine-free diet, a broader inhibition of serine transfer, or a PHGDH inhibitor. Furthermore, by quantifying scfluxes of serine-derived glycine formation and total serine consumption, ¹³C-scMFA estimated that neoplastic cells shuttle serine toward glycine formation more than astrocytes and neurons in most patients with GBM (Figure 5L) and suggests that inhibition of this reaction (perhaps via SHMT inhibitors) could selectively affect glioma cells in many patients. This is consistent with higher SHMT1 expression in patients with GBM of ICGC/TCGA pan-cancer dataset³² (Figure S5H).

To validate the ¹³C-scMFA serine model, we performed scRNA-seq using three mouse models (Figure 6A) with different responses to -SG diet: GBM12 (more resistant), GBM38, and HF2303 (more sensitive). In our studies, these human GBM models were engineered to express luciferase, allowing us to identify and monitor tumors in mice. After applying the baseline quality control procedure (Figure S6A), luciferase expression verified that 98% of the cells were aligned correctly to the human transcriptome (Figure S6B) and the rest were filtered out. Since ¹³C-scMFA serine model includes non-malignant cells to account for serine exchange in TME, we performed scRNA-seq on both brain and tumor tissues of GBM12, GBM38, and HF2303-bearing mice (Figure 6B). While applying clustering, differential expression analysis, and marker gene expression (Figure 6C–E, S6C), cell types including astrocytes, neurons, and neoplastic cells were identified (Figure 6F–G). Single-cell analysis showed 1.5% of brain cells clustered with tumor cells and expressing human genes (Figure 6H, S6D), which are neoplastic cells that invade from the tumor to the brain parenchyma (Figure 6G). To investigate serine metabolism in invading neoplastic cells and test our model’s competence in comparing scfluxes in multiple cell types and mouse models, we added invading neoplastic cells to ¹³C-scMFA model (Figure 5I). Cortex and tumor MIDs were assigned to astrocytes/neurons and neoplastic cells, because >96% of these cell populations belong to cortex and tumor samples, respectively (Figure 6G–I). Integrating MIDs with the expression of serine-related genes (Figure S6E) in ¹³C-scMFA model led to prediction of the highest glucose-derived serine synthesis in astrocytes of all mouse models (Figure 6J). This was further validated experimentally in Figure 2J. Furthermore, the neoplastic cells of GBM38 and HF2303 tumors were predicted to exhibit greater plasma serine uptake than those in GBM12 tumors (Figure 6K), explained by high TME-derived serine uptake in the latter model (Figure 6L). Hence, our model enabled distinction between exogenous serine sources and response to -SG diets. Additionally, our model showed that neoplastic cells use serine to synthesize glycine to a greater extent than astrocytes and neurons (Figure 6M).

Figure 6 – Validation of serine ¹³C-scMFA model.

(A) Validation of serine ¹³C-scMFA via stable isotope labeling experiments and scRNA sequencing from intracranial GBM12, GBM38, and HF2303-bearing mice infused with [U¹³C]-glucose. (B-C) UMAP representation of scRNAseq data colored by (B) mouse samples, (C) Louvain’s clusters. (D) Heatmap of top 20 differentially expressed genes in each cluster. (E) Expression of cell type-specific marker genes in clusters. (F) UMAP colored by cell types. (G) Fractional population of cell types and total number of cells passed quality control in mouse samples. (H) UMAP colored by brain and tumor tissues. Navy dots scattered in tumor represent invading neoplastic cells. (I) Serine ¹³C-scMFA model with invading neoplastic cells added. (J-M) Distribution of single-cell fluxes (scflux) estimated by serine ¹³C-scMFA model for (J) de novo serine synthesis, (K) plasma serine uptake, (L) TME-derived serine exchange flux, (M) ratio of serine-derived glycine formation to total serine consumption.

To investigate the heterogeneity of contributions of GMP sources in patients and different cell types, including HPRT1-dependent and IMPDH-dependent GMP pathways, we applied our ¹³C-scMFA model for purine metabolism (Figure 7A). We integrated scRNA-seq data from patients’ glioma samples with MIDs (Figure S7A, S4A–C). Given the distinct expression of purine pathway scores (de novo vs salvage) for myeloid vs. neoplastic cells (Figure 7B), and the dominancy of neoplastic and myeloid cells populations in glioma (Figure S5D), we focused on these cell types to deconvolute the metabolic activities of purine de novo and salvage pathways in patient tumors. Our results suggest that in most patients, IMPDH-dependent GMP synthesis is more active in neoplastic cells (Figure 7C), while HPRT1-dependent GMP synthesis is more active in myeloid cells (Figure 7D). The two routes of de novo GMP synthesis are through de novo IMP synthesis and HPRT1-dependent IMP synthesis. Although our results show that de novo IMP synthesis flux is usually higher in neoplastic cells (Figure S7B), IMP salvage pathway fluxes between myeloid and neoplastic cells vary patient-to-patient (Figure S7C). Other fluxes of our purine ¹³C-scMFA are shown in Figure S7D–I. In summary, these ¹³C-scMFA results agree with our CNN predictions where IMPDH-dependent GMP synthesis contributed more than HPRT1-dependent GMP synthesis in most patients (Figure 4P). Hence, both approaches suggest an IMPDH inhibitor such as MMF might be beneficial for patients with glioma. To validate ¹³C-scMFA purine model, we used MMF-sensitive GBM38 and MMF-resistant TRP mouse models. Single-cell analysis of TRP tumor tissues identified cell types including myeloid and neoplastic cells (Figure S7J–L). ¹³C-scMFA integrated scRNA-seq and ¹³C-MIDs of both mouse models (Figure S7M, S4M) and estimated a higher de novo GMP synthesis flux in GBM38 neoplastic cells compared to TRP, thus predicting a favorable response to MMF (Figure 7E).

Figure 7 – Single-cell flux quantification of purine metabolism with ¹³C-scMFA.

(A) Schematic of purine model for single cells. Myeloid and neoplastic cells are included in the model based on nucleotide synthesis-related gene expression. (B) Gene expression score for purine pathways calculated by Seurat module score. (C-D) Distribution of single-cell fluxes in myeloid and neoplastic cells for (C) IMPDH-dependent (de novo) GMP synthesis and (C) HPRT1-dependent salvage GMP synthesis in patients with glioma. (E) Validation of ¹³C-scMFA purine model. Estimated single-cell fluxes of de novo GMP synthesis flux in GBM38 and TRP models.

Discussion

In this work, we developed digital twins to identify metabolic pathway activity using ¹³C-isotope tracing data and training a CNN to predict relative fluxes of metabolite sources in patients with glioma. Moreover, we implemented a ¹³C-scMFA framework to quantify cellular fluxes and metabolite exchange fluxes within the TME. Our study has the advantage of pairing ¹³C-isotope tracing and scRNA-seq data to understand mechanisms behind metabolic crosstalk in TME, uptake of circulating metabolites, and metabolite synthesis and degradation in tumor vs adjacent tissue.

We applied our framework to predict individual patient responses to metabolically targeted therapies. Our model estimated a consistent dependence on serine de novo synthesis in cortex; however, we observed patient-to-patient heterogeneity in contribution of de novo serine synthesis, circulating serine uptake, and TME-derived serine uptake consistent with heterogeneity in glioma serine MIDs. The heterogeneity observed in PHGDH and PSAT1 expression in neoplastic cells of our patient scRNA-seq data were not correlated with M+3 serine-to-PG ratio in glioma tissue of our patients, reinforcing that higher gene expression does not necessarily imply higher metabolic rate. Surprisingly, PSPH average expression was correlated with glioma M+3 serine-to-PG ratio. Whether PSPH expression is adequate to drive serine synthesis can be explored further. By combining ¹³C-MIDs and scRNA-seq, ¹³C-scMFA offers improvements to other scFBA tools^18,33,34 that infer metabolic activity from gene expression alone.

Our model has the potential to guide precision metabolic therapies. Patient-specific heterogeneity was previously investigated in pancreatic ductal adenocarcinoma (PDAC) cells with distinct PHGDH expression and their dependence on exogenous serine³⁵. Exogenous serine-dependent PDAC cells restore growth when co-cultured with neurons³⁵ implicating TME-derived serine in proliferation. Other cancers such as breast cancer, melanomas, and brain metastases upregulate PHGDH and rely on de novo serine synthesis^36–39. Notably, the IDH-mutant glioma exhibited higher circulating serine uptake, whereas the other gliomas relied more on TME-derived serine and de novo serine, which should be further explored given small cohort size. Given the heterogeneity observed in patient molecular subtypes and clinical variations, we validated our models using GBM38 and GBM12 from the Mayo Clinic PDX database⁴⁰ incorporating proneural and classical molecular phenotypes according to methylation profiling, and the mesenchymal HF2303 model^41,42. These models incorporate varied genomic backgrounds spanning subtypes that reflect our patient cohort.

Although reversible SHMT flux was included in the serine simulation model, we did not estimate it in the metabolic CNN model since serine labeling from [U¹³C]-glycine infusion was negligible in mouse brain⁴³, indicating low uptake of circulating glycine or low SHMT-reverse flux. Additionally, GBM cell lines with high SHMT2 expression are sensitive to GLDC knockdown, where accumulation of glycine in these cells is toxic⁴⁴, implicating low SHMT-reverse flux in GBM cells. Since our MFA informed by CNN model estimated both SHMT flux in forward and reverse directions, we could identify a net forward SHMT flux for both glioma and cortex (Data S1), confirming three serine sources in glioma. ¹³C-scMFA estimated lower exogenous serine uptake in invading neoplastic cells compared to neoplastic cells of GBM12 and HF2303, consistent with lower expression of serine transporters SLC38A1 and SLC38A2. Future studies might explore whether invasion changes serine metabolism, alterations of serine pathways in immunocompetent mice, and metabolic interactions between immune and neoplastic cells given serine’s role in T cell activation and proliferation⁴⁵.

Due to low in vivo purine enrichment and complex R5P patterns, purine enrichment was primarily M+1 to M+5, rendering conventional methodology difficult. Thus, the digital twin approach allows estimation of both de novo and salvage synthesis even when conventional methods cannot. We validated our models via four strategies: (1) [U¹³C]-glucose infusion in tumor-bearing mice treated with MMF, (2) co-administration of [U¹³C]-glucose and [U¹³C]-serine in tumor-bearing mice treated with MMF, (3) ¹⁵N-amide-glutamine infusion in tumor-bearing mice treated with MMF, and (4) [U¹³C]-glucose infusion in multiple tumor models. Further, by performing scRNA-seq on GBM38 and TRP models, we validated our ¹³C-scMFA purine model. Although expression of de novo IMP and GMP synthesis genes is higher in TRP neoplastic cells, by integrating ¹³C-MIDs, our model predicted lower de novo GMP synthesis flux in TRP compared to GBM38. By quantifying IMPDH-independent and IMPDH-dependent GTP synthesis rates, our digital twin framework could identify which patients are likely to respond to MMF.

In summary, we implemented digital twins and ¹³C-scMFA frameworks to identify metabolic pathway activity in human tumors and adjacent tissues including different TME cell types. We applied this framework for purine and serine metabolism to understand which patients may benefit from different purine- or serine-targeting strategies. Expanding this framework to other tracers and pathways could lead to additional personalized therapies, while monitoring clinical progression of these patients over time could reveal which metabolic reactions drive tumor growth and recurrence. This knowledge will help us understand how cancers meet their metabolic demands for growth and how different cell types of the brain metabolically support one another.

Limitations of the study

Our study is subject to limitations of measuring metabolite concentrations in patients. Although we considered a wide range of metabolite pools in our MID simulation from available literature data, our model would predict more accurately if patient-specific concentration data were available. Although simulating nearly 1 million time-dependent enrichment profiles creates a comprehensive training dataset for our CNN model, a future patient might not fall into the generated isotopologue profiles. If this occurs, the digital twin should be updated to span isotopologues of all patients. Another limitation was low purine metabolite enrichment, adding to uncertainty around biological signal versus technical noise. We tried to overcome this challenge by imputing the purine enrichment data.

Stable isotope tracing studies generate a wealth of information. Inherent to the technology, it is impractical to include individual standards for every compound and often impossible to do so for every isobar. Therefore, the approach remains susceptible to errors, and overinterpretation of any single metabolite enrichment is considered. Our modeling method addresses this by integrating data across entire metabolic pathways, mitigating issues with any single metabolite. To further address this, we ran identical patient samples on multiple LC-MS platforms. As an example, glucose incorporation into serine varied between methods. Nonetheless, both platforms confirmed matching label ratios within molecular species (i.e., M+1 vs. M+3) and between tissue compartments (i.e., tissue vs. plasma). Cross-platform analysis can be a valuable approach to overcome limitations of any individual method.

Differences in resolution between scRNA-seq data and ¹³C-tracing data represented a challenge in ¹³C-scMFA development. We assigned bulk MIDs to single cells based on tissue of origin, which can introduce bias. To reduce bias, we normalized fluxes to gene expression while minimizing accumulation of isotopologues in cells. As spatial and single-cell metabolite tracing techniques advance, ¹³C-scMFA framework can be expanded to more accurately estimate scfluxes and metabolic crosstalk. Moreover, patient scRNA-seq data were limited to tumor samples. Hence, in serine ¹³C-scMFA model, we used gene expression of cortex-resident cells from Darmanis et al. assuming gene expression is similar among patients; however, this assumption is likely mitigated by cortex ¹³C-metabolic isotope tracing data.

Our small patient cohort size limits survival analysis. Some patients who underwent [U¹³C]-glucose tracing at time of initial tumor resection later received MMF concurrently with radiation and temozolomide in a parallel trial (NCT04477200). Patient 1, still living >3 years after GBM diagnosis and had an exceptional response to MMF, was predicted by ¹³C-scMFA to have near-complete dependence on IMPDH-mediated GMP synthesis in the neoplastic cells. By contrast, our ¹³C-scMFA model indicated lower IMPDH-driven GMP synthesis in neoplastic cells in patient 7, who died just over a year after diagnosis and had a poor response to MMF. Although both results suggest our model may inform treatment responses in patients, larger cohorts are needed to determine if these models can predict treatment responses.

Resource Availability

Lead Contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Deepak Nagrath (dnagrath@umich.edu).

Materials Availability

There are no newly generated materials in this paper.

Data and Code Availability

All data used to generate display items in this manuscript are available in Data S1. scRNA-seq data are publicly available for download and visualization via the Single Cell Portal: SCP3323 (patients), SCP3333 (PDXs), SCP3334 (TRP). scRNA-seq data will be available at Gene Expression Omnibus (GEO). The links and accession numbers for existing, publicly available datasets are listed in the key resources table. Seurat objects containing processed scRNA-seq and simulated data are available at https://doi.org/10.5281/zenodo.17373726. Codes generated in this study were deposited at https://github.com/baharm1/ML_MFA.

Key resources table

REAGENT OR RESOURCE	SOURCE	IDENTIFIER
Biological samples
GBM38	Vaubel et al.40	N/A
GBM12	Vaubel et al.40	N/A
HF2303	Berezovsky et al.41 Ye et al.46	N/A
TRP	Schmid et al.24 McNeill et al.25	N/A
Chemicals, peptides, and recombinant proteins
L-Glutamine (amide-15N, 98%)	Cambridge Isotope Laboratories	NLM-557-PK
D-Glucose (13C6, 99%)	Cambridge Isotope Laboratories	CLM-1396-PK
L-Serine (13C3, 99%)	Cambridge Isotope Laboratories	CLM-1574-H-PK
Mycophenolate mofetil	SelleckChem	Cat#S1501
Deposited data
Patient scRNA-seq data	This study	https://singlecell.broadinstitute.org/single_cell/study/SCP3323/digital-twins-for-in-vivo-metabolic-flux-estimations-in-patients-with-brain-cancer-patient-data
PDX scRNA-seq data (GBM12, GBM38, HF2303-bearing mice)	This study	http://singlecell.broadinstitute.org/single_cell/study/SCP3333/digital-twins-for-in-vivo-metabolic-flux-estimations-in-patients-with-brain-cancer-pdx-data
TRP GBM tumor	This study	https://singlecell.broadinstitute.org/single_cell/study/SCP3334/digital-twins-for-in-vivo-metabolic-flux-estimations-in-patients-with-brain-cancer-trp-mouse-data
Processed scRNA-seq data and simulated data	This study, Zenodo47	https://doi.org/10.5281/zenodo.17373726
Data S1 – source data	This study	Data S1
mRNA expression of glioma samples	ICGC/TCGA pan-cancer dataset (2020)32	https://www.cbioportal.org/study/summary?id=pancan_pcawg_2020
scRNA-seq of tumor and adjacent cortex	Darmanis et al.15	http://www.gbmseq.org/; GSE84465
Patient and mouse 13C-enrichment data	Scott et al.9	Supplementary Dataset
Experimental models: Organisms/strains
Mouse: B6.129S7-Rag1tm1Mom/J	The Jackson Laboratory or bred in-house	RRID:IMSR_JAX:002216
Mouse: C57BL/6J	The Jackson Laboratory	RRID:IMSR_JAX:000664
Software and algorithms
Codes generated in this study including single-cell analysis, metabolic interaction analysis, modified scFEA, 13C-scMFA, flux and MID simulations, and metabolic CNN	This study	https://github.com/baharm1/ML_MFA
IsoCorrectoR (version 1.24.0)	Heinrich et al.48	https://www.bioconductor.org/packages/release/bioc/html/IsoCorrectoR.html
Skyline (version 24.1.0.199)	MacLean et al.49	https://skyline.ms/project/home/software/skyline/begin.view
Graphpad Prism (version 10)	GraphPad Software	RRID: SCR_002798; https://www.graphpad.com/features
Cell Ranger (v7.1.0 and v8.0.0)	Zheng et al.50	https://www.10xgenomics.com/support/software/cell-ranger/latest
Adobe Illustrator	Adobe Inc.	RRID:SCR_010279; https://www.adobe.com/products/illustrator.html
BioRender	BioRender	RRID:SCR_018361; https://www.biorender.com/
R (version 4.2.2)	R Core Team	https://www.r-project.org/
Seurat (version 4.2.0)	Hao et al.51	RRID: SCR_007322; https://satijalab.org/seurat
dplyr (version 1.1.2)	Wickham et al.52	RRID:SCR_016708; https://cran.r-project.org/package=dplyr
tidyr (version 1.3.0)	Wickham et al.53	RRID:SCR_017102; https://cran.r-project.org/package=tidyr
ggplot2 (version 3.4.2)	Wickham54	RRID:SCR_014601; https://cran.r-project.org/package=ggplot2
patchwork (version 1.1.2)	Pedersen55	RRID:SCR_000072; https://cran.r-project.org/package=patchwork
reshape2 (version 1.4.4)	Wickham56	RRID:SCR_022679; https://cran.r-project.org/package=reshape2
Polychrome (version 1.5.1)	Brock et al.57	https://cran.r-project.org/package=Polychrome
scales (version 1.2.1)	Wickham et al.58	RRID:SCR_019295; https://cran.r-project.org/package=scales
DropletUtils (version 1.18.1)	Griffiths et al.59	RRID:SCR_026136; https://bioconductor.org/packages/release/bioc/html/DropletUtils.html
scrabble (version 1.0.0)	Neftel et al.30	https://github.com/jlaffy/scrabble
GSEABase (version 1.60.0)	Morgan et al.60	https://www.bioconductor.org/packages/release/bioc/html/GSEABase.html
harmony (version 0.1.1)	Krosunsky et al.61	RRID:SCR_022206; https://github.com/immunogenomics/harmony
DoubletFinder (version 2.0.3)	McGinnis et al.62	RRID:SCR_018771; https://github.com/chris-mcginnis-ucsf/DoubletFinder
scCustomize (version 1.0.0)	Marsh63	RRID:SCR_024675; https://samuel-marsh.github.io/scCustomize/
RColorBrewer (version 1.1-3)	Neuwirth64	RRID:SCR_016697; https://cran.r-project.org/package=RColorBrewer
Matrix (version 1.5-1)	Bates et al.65	https://cran.r-project.org/package=Matrix
stringr (version 1.5.0)	Wickham66	RRID:SCR_022813; https://cran.r-project.org/package=stringr
cowplot (version 1.1.1)	Wilke67	RRID:SCR_018081; https://cran.r-project.org/package=cowplot
Rmagic (version 2.0.3)	van Dijk et al.68	https://cran.r-project.org/src/contrib/Archive/Rmagic/
ggpubr (version 0.4.0)	Kassambara69	RRID:SCR_021139; https://cran.r-project.org/package=ggpubr
introdataviz (version 0.0.0.9003)	Nordmann et al.70	https://github.com/PsyTeachR/introdataviz
gghalves (version 0.1.4)	Tiedermann71	https://cran.r-project.org/package=gghalves
see (version 0.8.0)	Lüdecke et al.72	https://cran.r-project.org/package=see
readxl (version 1.4.2)	Wickham et al.73	https://cran.r-project.org/package=readxl
RcmdrMisc (version 2.7-2)	Fox74	https://cran.r-project.org/package=RcmdrMisc
pheatmap (version 1.0.12)	Kolde et al.75	RRID:SCR_016418; https://cran.r-project.org/package=pheatmap
corrplot (version 0.92)	Wei et al.76	RRID:SCR_024683; https://cran.r-project.org/package=corrplot
ggbeeswarm (version 0.7.2)	Clarke et al.77	RRID:SCR_026875; https://cran.r-project.org/package=ggbeeswarm
Python (version 3.8 and 3.11)	Python Software Foundation	https://www.python.org
Anaconda (conda 23.7.2)	Anaconda Software Distribution	https://anaconda.com/
cuda 12.1.1	NVIDIA	https://pypi.org/project/cuda-python/
torch 2.2.1+cu121	Ansel et al.78	RRID:SCR_018536; https://pytorch.org/
magic (version 3.0.0)	van Dijk et al.68	https://github.com/KrishnaswamyLab/MAGIC
pandas 2.0.3	McKinney79	RRID:SCR_018214; https://pandas.pydata.org/
numpy 1.24.4 and 1.26.3	Harris et al.80	RRID:SCR_008633; https://numpy.org/
scipy 1.10.1	Virtanen et al.81	RRID:SCR_008058; https://scipy.org/
scikit-learn 1.3.0	Pedregosa et al.82	RRID:SCR_002577; https://scikit-learn.org/stable/
optuna 3.1.0	Akiba et al.83	https://optuna.org/
joblib 1.3.0	Joblib Developers84	https://pypi.org/project/joblib/
matplotlib 3.7.2 and 3.8.3	Hunter85	RRID:SCR_008624; https://matplotlib.org/
plotly 5.15.0	Plotly Technologies Inc.	RRID:SCR_013991; https://plotly.com/
MEBOCOST (v1.0.4)	Zheng et al.16	https://github.com/kaifuchenlab/MEBOCOST
scFEA (v1.1-beta0.1)	Alghamdi et al.18	https://github.com/changwn/scFEA
Other
Baker Amino Acid Diet	TestDiet	Cat#5CC7
Modified Baker Amino Acid Diet without serine or glycine	TestDiet	Cat#5BJX

STAR★Methods

Experimental model and study participant details

Animal models

All animal experiments were approved by the Institutional Animal Care and Use Committee at the University of Michigan and conducted with general care and husbandry from the University of Michigan Unit for Laboratory Animal Medicine. Mice were aged 4–12 weeks at the start of experiments. Male and female C57BL/6 mice (obtained from Jackson Laboratory) and B6.129S7-Rag1^tm1Mom/J mice (obtained from Jackson Laboratory or bred in-house) were housed in specific-pathogen-free conditions at a temperature of 74 °F with relative humidity between 30–70% and 12 h light–dark cycles.

Cell culture models

Primary astrocytes and neurons from neonatal mice were harvested and cultured as described⁸⁶ for subsequent experiments. Briefly, primary cells were prepared from postnatal day 0 mice pups. The Hippocampus and striatum were separated for primary neuron culture and plated in Gibco Neurobasal medium supplied with 2% B27 supplement and 1% glutamine. The cerebral cortex tissues were separated for primary astrocyte culture, which were cultured with DMEM containing 10% FBS and 4 mM glutamine. These primary cells were cultured for at least 7 days and media was changed every two days. GBM38 explants were extracted from an in vivo PDX tumor and propagated in DMEM containing 10% FBS and a total L-glutamine concentration of 4 mM for less than 20 passages prior to experiments. All cells were cultured in MEM with 10% dialyzed FBS for in vitro experiments as described below.

Human participants

Data were analyzed from a cohort of eight adult patients with gliomas (six males and two females) with informed consent in a previous study approved by the Institutional Review Board of the University of Michigan. Demographic analyses are limited by the small number of patients.

Method details

Stable isotope labeling in vivo

Catheters were surgically implanted into the jugular vein and carotid artery of B6.129s7-RAG1 tm/Mom/J mice bearing intracranial GFP+ GBM38 tumors or C57BL/6 mice bearing GFP+ TRP tumors^{9,14,24,25,40,87,88}. For infusion experiments in which mice received vehicle or MMF treatment, a third line was placed into the stomach to avoid gavage-related complications with local cannulas. Five days post-surgery, administration of MMF at indicated dosages into the gastric line commenced. Stable isotope tracers were infused as previously described via the intravenous line into conscious, unrestrained mice⁹. Infusions of uniformly labeled ¹³C-glucose were performed using a bolus of 0.4 mg/g followed by a continuous infusion of 0.012 mg/g/min. Infusions of ¹⁵N-amide-glutamine were performed using a bolus of 0.28 mg/g followed by a continuous infusion of 5 μg/g/min. Infusion times (bolus and continuous infusions) totaled 4 h. Blood samples were collected via the arterial line and used to prepare plasma samples. At the end of infusions, mice were anesthetized with intravenous ketamine (50 mg/kg) and sacrificed by decapitation followed by immediate extraction of tumor tissue and cortical tissue from the opposite hemisphere on dry ice. A fluorescent bulb was used to separate GFP+ tumor tissue from the brain. Tissues were immediately flash frozen in liquid nitrogen. Samples were homogenized in 80% methanol at −80°C and clarified by centrifugation. Supernatants were dried by nitrogen purging, reconstituted in 1:1 methanol/water and analyzed by LC-MS using an Infinity Lab II UPLC coupled with either a 6545 or 6230 QTOF mass spectrometer (Agilent Technologies, Santa Clara, CA) operated by the University of Michigan Metabolomics Core. Full chromatography methods and gradients were as described previously⁹. Data were analyzed and corrected for natural isotope abundance using Agilent MassHunter Profinder version 10.0. Control plasma and brain tissue from subjects not undergoing ¹³C or ¹⁵N tracer infusion were analyzed with each run to minimize the risk of spurious label peak detection, though the potential for contaminating isobars present only in traced mice and patients remains.

Dual in vivo stable isotope tracing was performed using intracranial GBM38-bearing mice without surgical catheter placement, with mice administered 4 daily doses of MMF (150 mg/kg, once-per-day oral administration) prior to labeling. Two hours after the fourth MMF treatment, in vivo labeling was initiated. In vivo labeling was performed by serial intraperitoneal injections of [U¹³C]-glucose (2 g/kg) and U¹³C-serine (1.2 μmol/g) every 20 min until sacrifice. Two hours after the first injection, mice were sacrificed using a lethal dose of isoflurane via the drop method, followed by tissue harvests and sample preparation as described above. Metabolites were detected with a Thermo Scientific Orbitrap IQ-X Tribrid mass spectrometer using an injection volume of 3 μL. The Waters ACQUITY UPLC BEH Amide 2.1 X 100 mm, 1.7μm column (186004801) was used. The column was held at 30 °C; the flow rate was 0.2 ml/min. Mobile Phase A was comprised of 0.1% Ammonium hydroxide in purified deionized water with 20 mM Ammonium carbonate; Mobile Phase B was comprised of pure acetonitrile. Each sample was subjected to a linear gradient as follows: 0–0.5 min 85% B, 0.5–15 min 15% B, 15–17 min 15% B, 17–17.1 min 85% B, 17.1–22 min 85% B. Metabolite data were extracted in Skyline and manually integrated according to an in-house list of standard m/z and retention times. Natural isotope abundance correction was performed with IsocorroctoR.

Stable isotope tracing in vitro

Primary astrocytes and neurons from neonatal mice were separated and cultured as described in a previous report⁸⁶. Primary astrocytes, neurons, and GBM38 explants were seeded at 5 × 10⁵ cells per well in 6-well plates. Cells were then incubated with MEM containing either [U¹³C]-glucose (25 mM) or U¹³C-serine (0.4 mM) and dialyzed FBS. Media samples and cell samples were collected at indicated timepoints (Figure 2H) and then processed and analyzed for LC-MS using the IQ-X Tribrid mass spectrometry platform described above. Serine M+3 abundance at time 0 was measured and set as the reference point. Serine M+3 abundance was measured in the media of primary mouse astrocytes and neurons, and patient-derived GBM38 cells after 5 minutes. The subtraction of these values represents the extent of consumption of serine M+3 from the media of these cells (Figure 2J). This analysis is shown in Data S1.

Human tumor specimen collection

Under an institutional review board (IRB)-approved study in accordance with recognized ethical guidelines, brain tumor specimens were previously collected from patients perioperatively infused with uniformly labeled ¹³C-glucose at the University of Michigan using MRI-imaged guidance technology to localize specimen within enhancing and non-enhancing tumor and adjacent cortex⁹. This research was in full compliance of all pertinent ethical regulations for research with human biospecimens, and all data were de-identified (IRB HUM00175135).

Single-cell RNA-seq data collection

Human tumor samples were dissociated into single cells utilizing Accutase dissociation reagent (Gibco, NH). Cells were passed through a 70μm strainer (Alkali Inc), centrifuged, and resuspended followed by application of RBC lysis buffer (Biolegend). Intracranial syngeneic TRP GBM tumors and patient-derived GBM tumors (GBM12, GBM38, and HF2303) were harvested and dissociated using Collagenase Type II (Invitrogen, 17101015) with rotation at 37°C. The cell suspension was passed through a 40um strainer (Fisherbrand, 22363547), centrifuged, and resuspended followed by application of RBC lysis buffer (Biolegend).

Single cell suspensions were subjected to counting on the LUNA Fx7 Automated Cell Counter (Logos Biosystems) and diluted to a concentration of 1000 cells/μL. Single cell 3’ gene expression libraries were generated using the 10x Genomics Chromium instrument following the manufacturer’s protocol. In brief, suspensions were loaded onto the 10x chip along with reverse transcription (RT) master mix and appropriate gel beads. Following generation of single-cell gel bead-in-emulsions (GEMs), reverse transcription was performed, and the resulting Post GEM-RT product was cleaned up and the cDNA amplified. cDNA was subjected to enzymatic fragmentation and size selection to optimize the cDNA size prior to final library construction following the manufacturer’s protocol (10x Genomics; 3’ v3 (patient) and 3’ v4 (mouse)). Final library quality was assessed using the LabChip GX (PerkinElmer). Pooled libraries were then subjected to paired-end sequencing according to the manufacturer’s protocol (Illumina NovaSeq 6000). Bcl2fastq2 Conversion Software (Illumina) was used to generate de-multiplexed fastq files and the Cell Ranger Pipeline (10x Genomics) was used to align reads and generate count matrices.

Single-cell RNA sequencing analysis

Raw sequencing reads of patient samples were aligned to GRCh38-2020-A human reference transcriptome using Cell Ranger (v7.1.0) with default parameters (including intronic reads). To identify human and mouse cells in patient-derived GBM models including GBM12, GBM38, and HF2303 samples, cells were aligned to a combined human and mouse reference transcriptome GRCh38_and_GRCm39-2024-A with the addition of luciferase sequence and the syngeneic TRP GBM cells were aligned to mouse reference transcriptome GRCm39-2024-A with the addition of luciferase sequence using Cell Ranger (v.8.0.0).

The filtered gene-barcode matrix which excludes background noise was generated based on the barcode rank plot. The filtered count matrices were loaded and merged into a Seurat object (v4.1.2) separately for patient samples and PDXs. For patient samples, low-quality single cells containing < 500 detected genes or < 1000 UMI counts or > 12% mitochondrial transcripts or > 50% ribosomal transcripts were filtered out. The doublet rate and number of recovered cells (10X Genomics Chromium Single Cell 3’ Reagent Kit v3) were regressed to find the doublet rate for each sample. DoubletFinder (v2.0.3) was used to predict the potential doublets in scRNA-seq data⁶². Furthermore, cells with > 100,000 UMI counts or > 10,000 detected genes were removed. For PDX samples and TRP tumor samples, low-quality cells were excluded from the data based on the following criteria: < 500 detected genes or < 1000 UMI counts or > 12% mitochondrial transcripts or > 100,000 UMI counts or > 10,000 detected genes. Luciferase expression verified that 98% of the cells were aligned correctly to the human transcriptome. The remaining 20,057 single cells were considered human cells if: the expression of luciferase > 0 or the percentage of alignment to human reference transcriptome (GRCh38) > 90%; or mouse cells if luciferase is not expressed and percentage of alignment to human reference transcriptome < 10%. In PDX samples, all the neoplastic cells must be aligned to human transcriptome (12,829 cells) and all non-neoplastic cells must be aligned to mouse transcriptome (7,070 cells). After annotating neoplastic cells and non-neoplastic cells, 158 cells categorized to human non-neoplastic cells were also filtered out.

Following Seurat workflow⁵¹, the remaining single cells were log-normalized to the library size with the scale factor of 10,000 and scaled using Seurat package (v4.2.0). The first 2000 highly variable genes were used in principal component analysis to reduce the dimensionality of features. To correct the batch effect of PC modalities between different samples, Harmony (v0.1.1) was used⁶¹. The first 35 batch corrected PCs (harmony modalities) were used to find neighbors, clusters, and uniform manifold approximation and projection (UMAP). Different cluster resolutions (0.1, 0.5, 0.8) were selected based on the refinement needed for cell annotations. scCustomize (v1.0.0, RRID:SCR_024675) was used to create plots. FindAllMarkers function identified positive cluster-specific marker genes which were used to examine cell type annotations. To identify cell types in our scRNA-seq data, we used two levels of GBmap marker genes²⁸. GBmap level-1 annotations including marker genes of neoplastic and non-neoplastic cells were passed through Seurat::AddModuleScore function and the overall module score for neoplastic and non-neoplastic cells were visualized by Seurat::FeaturePlot. Level-1 annotation identified cluster 0 as non-neoplastic cells which then was used in CopyKAT (v1.1.0) analysis²⁹ as known normal cells with other arguments set to default. Similar to level-1 annotations, we calculated GBmap level-2 annotations which identified subtypes of non-neoplastic cells (myeloid, oligodendrocyte, vascular, and lymphoid). Finally, we collected marker genes of various cell types from^89–91 and explored marker gene expressions in our identified cell types. In addition to neoplastic cells (EGFR, GFAP, AQP4, VIM, MT1X, PDGFRA, BCAN, VCAN), other clusters including myeloid (CX3CR1, P2RY12, TGFBI), oligodendrocyte (MBP, MOBP, MOG, PLP1), endothelial (PECAM1, VWF, TEK), pericyte (PDGFRB, ACTA2), and lymphoid (CD3D, NKG7, PTPRC, MZB1, MS4A1) were identified (Figure 5D–F). To identify neoplastic subtypes, we made a score of Neftel’s cell states³⁰ for each neoplastic cell using AddModuleScore function. The scores of AC-like, MES-like, OPC-like, and NPC-like cells were used to create a butterfly plot using scrabble package in R. Molecular subtype classification was previously described⁹ for all single cells. Here, the AUCell gene set enrichment scores⁹² based on 50 genes per subtype⁹³ were shown for patients’ neoplastic cells and other cell types.

Single cell metabolic interaction analysis in an independent cohort of GBMs

To study metabolic interactions between cell types in the glioma tumor microenvironment, we selected Darmanis et al.’s scRNA-seq dataset (GSE84465) since it includes both tumor and periphery samples¹⁵. We reanalyzed this dataset following their scRNA-seq analysis protocol to control quality of reads and annotate cell types. 3589 cells passed quality control. Raw reads were log-normalized with scale factor of 10,000 and saved in h5 format to be imported in MEBOCOST¹⁶. We curated reactions related to serine and added them to MEBOCOST default metabolic model. A MEBOCOST object was created from the normalized reads with cutoff_prop=0.25, and sensor types including receptors, transporters, and nuclear receptors. To infer cell type metabolic interactions a permutation test with 1000 shuffles was performed with Benjamini-Hochberg’s correction. The default communication score (metabolite presence × transporter expression) was used.

Integrated single cell flux balance analysis and metabolic flux analysis

We adopted the idea of using neural network to quantify fluxes from scFEA¹⁸. We curated a metabolic model for each cell type based on the RNA expression of metabolite transporters, and enzymes producing/consuming that metabolite. The gene expression of cell types is fed into a multilayer perceptron (MLP) to generate fluxes. Fluxes are optimized to minimize the accumulation of metabolites and MIDs.

Here, we denote:

• k: number of metabolites related to cell types

• k’: number of metabolites related to tissue

• r: number of reactions

• g: number of genes in the metabolic model

• c: number of cells

• S: stoichiometry matrix

• ct: cell type

• G: gene expression

• M: mass isotopologue distribution (MID)

• m: isotopomer distribution

• i: number of isotopes in a metabolite (M+i)

Metabolic and exchange reactions

Reactions and enzymes associated with each reaction were selected from Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway database⁹⁴. Reactions were categorized into production, consumption, and exchange of a target metabolite (e.g., serine). Similar to scFEA, we assumed unidirectionality of metabolic reactions. Our metabolic map includes production and consumption reactions for each cell type. To assume the direction of exchange reactions in different cell types, we considered MEBOCOST cell type connectivity. In addition, we defined a metabolite accumulation score (MAS) for cell type ($ct$) as follows:

$${\mathbf{M}\mathbf{A}\mathbf{S}}_{\mathbf{c}\mathbf{t}}=\sum _{c\in ct}\left(\sum _{g\in \mathit{\text{prod}}.}{\mathbf{G}}_{\mathbf{g},\mathbf{c}}-\sum _{g\in \mathit{\text{cons}}.}{\mathbf{G}}_{\mathbf{g},\mathbf{c}}\right)$$

Where $G_{g,c}$ is the gene expression matrix imputed by MAGIC⁶⁸. The first term is the sum of expression of genes producing a metabolite and the second term is the sum of expression of genes consuming the metabolite. The intuition behind this score is that a cell type with a higher score has accumulation of a metabolite and it may get secreted into tumor microenvironment, whereas a cell type with a low score may be unable to produce that metabolite and need to uptake it from the tumor microenvironment. Gene sets assigned to the exchange reactions include solute carrier transporters (SLCs) were found in Transporter Classification Database⁹⁵. The metabolic model is curated for cell types with the highest and lowest MAS and malignant cell types. Algorithm 1 describes curation of a metabolic model. An example of exchange metabolite is serine where in the metabolic model exchange reactions need to be defined. Based on MEBOCOST, MAS, and modified scFEA analysis we defined the directionality of exchange reactions between cell types and added them to producing/consuming reactions to create metabolic models for each cell type. For metabolites such as GMP which cannot be transported, we calculated reaction score for each cell type using Seurat::AddModuleScore of associated gene expression. To reduce the complexity of metabolic model, cell types with distinguished reaction scores were selected and a metabolic model for each cell type was created that includes producing/consuming reactions.

Algorithm 1:

Curation of a metabolic model

Input: scRNA-seq data (normalized read counts and cell types)
Output: metabolic model
1.	Define a target metabolite based on literature review.
2.	Find reactions and enzymes related to the target metabolite from KEGG pathway database and Recon3D94,96.
3.	If the target metabolite is a TME exchange metabolite:
	3.1.	Calculate MAS and MEBOCOST accumulation score for cell types in the TME.
	3.2.	Subset cell types based on MAS and communication score (Figure 2A–B).
	3.3.	Define the direction of exchange reactions.
	3.4.	Curate a metabolic model by adding exchange reactions to previously defined KEGG reactions for selected cell types.
4.	Otherwise,
	4.1.	Calculate reaction module scores and subset cell types (Figure 7B).
	4.2.	Create a metabolic model for selected cell types based on previously defined KEGG reactions.

Serine metabolic and exchange reactions

Serine can be synthesized from phosphoglycerate through a cascade of enzymes including PHGDH, PSAT1, and PSPH. Serine can produce other metabolites such as glycine, pyruvate, D-serine, cysteine, protein serine, 3-dehydrosphinguanine, and phosphotidylserine through SHMT1/SHMT2, SDS/SDSL, SRR, CBS, SARS/SARS2, SPTLC1/SPTLC2/SPTLC3, PTDSS1/PTDSS2, respectively. For serine exchange reactions (uptake and secretion), we collected serine transporters including SLC1A4, SLC1A5, SLC3A2, SLC6A9, SLC6A14, SLC7A8, SLC7A10, SLC12A4, SLC25A1, SLC25A15, SLC25A28, SLC36A1, SLC38A1, SLC38A2, SLC38A4, SLC38A5, SLC38A7^97,98.

Quantification of TME exchange flux using scRNA-seq data

Although MAS and MEBOCOST analyses suggested potential metabolite sender and receiver cell types, they do not quantify the secretion and uptake of a metabolite. Hence, we adopted the scFEA algorithm to include the exchange fluxes within the TME (Algorithm 2). To quantify inter- and intracellular fluxes, we modified scFEA to include cell type-specific fluxes and introduce extracellular metabolites such that there is no accumulation of extracellular metabolites in the TME.

Algorithm 2:

Modified scFEA

Inputs:
	• Stoichiometry matrix (coefficients of fluxes in balance equations) ${\mathbf{S}}_{\mathbf{k}\times \mathbf{r}}$
	• Gene expression matrix ${\mathbf{G}}_{\mathbf{g}\times \mathbf{c}}$
	• Cell ids of cell types ${\mathbf{c}\mathbf{t}}_{\mathbf{c}\times \mathbf{1}}$
	• Associated genes for reactions
Outputs:
	• Single cell fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$
	• Objective values
Prepare training data
1.	Preprocess the gene expression matrix with the procedure described below $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t})\times \mathbf{c}}\right)$.
2.	Impute the preprocessed gene expression using MAGIC68 $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t})\times \mathbf{c}}\right)$.
3.	Scale sum of imputed gene expression for each cell (${\overline{\mathbf{G}}}_{\mathbf{c}}$):
	${\overline{\mathbf{G}}}_{\mathbf{c}}=\frac{{\sum }_{g,ct}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}{\frac{1}{C}{\sum }_c{\sum }_{g,ct}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}$
	In other words, ${\overline{\mathbf{G}}}_{\mathbf{c}}$ is the sum of imputed gene expression for each cell divided by the mean of total imputed gene expression of all cells.
4.	Reconstruct imputed gene expression as described below $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}\right)$.
5.	Calculate mean of imputed gene expression for each reaction (${\tilde{\mathbf{G}}}_{\mathbf{r}\times \mathbf{c}}$). This step corrects for number of genes associated with a reaction.
	${\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}=\frac{{\sum }_{g,ct~r}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}{{\sum }_{g,ct~r}\mathbf{1}}$
Estimate single cell fluxes using neural network
6.	Setup training data including ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}},{\overline{\mathbf{G}}}_{\mathbf{c}}$, and ${\tilde{\mathbf{G}}}_{\mathbf{r}\times \mathbf{c}}$.
7.	Initialize each flux $\left(v\right)$ through a two-layer perceptron which returns single cell fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$ given ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}$ as described below.
8.	Optimize fluxes to minimize the sum of the four loss terms:
	a. Metabolite accumulation in cells and TME using the stoichiometry matrix:
	$L_1={\alpha }_1\sum _c\sum _{k\in \mathit{\text{int}}.}{\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}}{\mathbf{V}}_{\mathbf{r},\mathbf{c}}\right)}^2+{\alpha }_1\sum _{k,r\in \mathit{\text{exc}}.}{\left(\sum _{ct\in \mathit{\text{sec}}.}\frac{{\sum }_c{\mathbf{V}}_{\mathbf{r},\mathbf{c}}^{\mathbf{r}\in \mathbf{s}\mathbf{e}\mathbf{c}.}}{{\sum }_{c\in ct}\mathbf{1}}-\sum _{ct\in up.}\frac{{\sum }_c{\mathbf{V}}_{\mathbf{r},\mathbf{c}}^{\mathbf{r}\in \mathbf{u}\mathbf{p}.}}{{\sum }_{c\in ct}\mathbf{1}}\right)}^2$
	Where the first term represents cellular flux balance equations for intercellular metabolites and the second term represents exchange flux balances in the TME which sets the secretion of metabolite k from sender cell types ($ct\in \mathit{\text{sec}}$.) equal to its uptake by receiver cell types ($ct\in up$.).
	b. Negative fluxes:
	$L_2={\alpha }_2\sum _c\sum _r\left(\left|{\mathbf{v}}_{\mathbf{r},\mathbf{c}}\right|-{\mathbf{v}}_{\mathbf{r},\mathbf{c}}\right)$
	scFEA assumes fluxes are non-negative and unidirectional.
	c. Flux variations for cells with similar metabolic activity:
	$L_3={\alpha }_3\sum _c{\left(\sum _r{\mathbf{V}}_{\mathbf{r},\mathbf{c}}-{\overline{\mathbf{G}}}_{\mathbf{c}}\right)}^2$
	d. Incoherence between flux and reaction’s associated genes
	$L_4={\alpha }_4\sum _c\sum _r\left(1-\mathit{\text{corr}}\left({\mathbf{V}}_{\mathbf{r},\mathbf{c}},{\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}\right)\right)$
	Where ${\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4$ are Lagrange multipliers which are set empirically similar to scFEA18. Optimization stops when there is no improvement observed in the total loss value and the weights of MLP become fixed.
9.	Estimate fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$: With optimized weights, MLP can estimate single cell fluxes given ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}$.

Quantification of serine exchange reactions (modified scFEA) using gene expression

To understand whether the exogenous serine flux has a microenvironmental component in addition to the plasma serine, we aimed to quantify the serine exchange fluxes in three cell types including astrocytes, neurons, and neoplastic cells using Darmanis et al.’s scRNA-seq dataset and single cell flux balance analysis. MEBOCOST and MAS analyses suggested that astrocytes can be a microenvironmental serine source. Hence, we defined the metabolic and exchange reactions in the microenvironment as shown in Table S1. Fluxes were generated through an MLP using the associated gene expression and balanced to minimize the accumulation of intra- and extracellular metabolites. The balance equations for cellular fluxes are shown in Table S2. Lagrange multipliers were set to ${\alpha }_1=1.5$, ${\alpha }_2=1$, ${\alpha }_3=1$, ${\alpha }_4=0.01$.

Quantification of intra- and inter cellular fluxes using integrated scRNA-seq and plasma and tissue MIDs

Modified scFEA helps in assuming the direction of TME exchange fluxes, but since it uses the scRNA-seq solely and the associated genes for TME exchange fluxes and circulating metabolite uptake fluxes are the same (both uses transporter genes), it is unable to estimate the circulating flux. Integration of scRNA-seq data with bulk MIDs helps in quantifying TME exchange fluxes as well as circulating metabolite uptake fluxes. To account for exchange metabolite MIDs, we assumed that TME metabolites arise from the sender cell types (based on MAS, MEBOCOST, and modified scFEA) and they have same MIDs as the tissue which include the sender cell type majorly. By integrating these MIDs into the scRNA-seq data, ¹³C-scMFA (Algorithm 3) is able to distinguish between exogenous metabolite sources (i.e., circulating and TME) although the associated genes for these fluxes are similar.

Algorithm 3:

¹³C-scMFA

Inputs:
	• Stoichiometry matrix (coefficients of fluxes in balance equations) ${\mathbf{S}}_{\mathbf{k}\times \mathbf{r}}$
	• Isotopologue balance matrix as described below (coefficients of fluxes in isotopologue balance equations)
	• Gene expression matrix ${\mathbf{G}}_{\mathbf{g}\times \mathbf{c}}$
	• Percent enrichment of MIDs in normal and tumor tissues ${\mathbf{M}}_{\left({\mathbf{k}}^{\prime }\times \mathbf{i}\right)\times \mathbf{1}}$
	• Cell ids of cell types ${\mathbf{c}\mathbf{t}}_{\mathbf{c}\times \mathbf{1}}$
	• Associated genes for reactions
Outputs:
	• Single cell fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$
	• Objective values
Prepare training data
1.	Preprocess the gene expression matrix with the procedure described below $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t})\times \mathbf{c}}\right)$.
2.	Impute the preprocessed gene expression using MAGIC68 $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t})\times \mathbf{c}}\right)$.
3.	Scale sum of imputed gene expression for each cell (${\overline{\mathbf{G}}}_{\mathbf{c}}$):
	${\overline{\mathbf{G}}}_{\mathbf{c}}=\frac{{\sum }_{g,ct}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}{\frac{1}{C}{\sum }_c{\sum }_{g,ct}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}$
	In other words, ${\overline{\mathbf{G}}}_{\mathbf{c}}$ is the sum of imputed gene expression for each cell divided by the mean of total imputed gene expression of all cells.
4.	Reconstruct imputed gene expression as described previously $\left({\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}\right)$.
5.	Calculate mean of imputed gene expression for each reaction (${\tilde{\mathbf{G}}}_{\mathbf{r}\times \mathbf{c}}$). This step corrects for number of genes associated with a reaction.
	${\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}=\frac{{\sum }_{g,ct~r}{\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}),\mathbf{c}}}{{\sum }_{g,ct~r}\mathbf{1}}$
6.	Assign bulk MIDs (${\mathbf{M}}_{\left({\mathbf{k}}^{\prime }\times \mathbf{i}\right)\times \mathbf{1}}$) to single cells based on the location of cells. If a cell type is in tumor periphery, cortex MIDs are assigned, otherwise, glioma MIDs are assigned. Output of this step has a shape of (${\mathbf{M}}_{(\mathbf{k}\times \mathbf{i})\times \mathbf{1}}$).
7.	Cell type MIDs are replaced in the isotopologue balance matrix and multiplied by stoichiometry matrix to generate the cellular metabolite isotopic balance equations. In other words, this step calculates the Hadamard product of ${\mathbf{S}}_{\mathbf{k}\times \mathbf{r}}\odot {\mathbf{M}}_{\mathbf{k}\times \mathbf{r}}^i$ where k and i represents cellular metabolites, and the number of isotopologues, respectively. The final isotopologue balance matrix has a shape of (number of metabolites × number of isotoplogues) × number of reactions.
Estimate single cell fluxes using neural network
8.	Setup training data including ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}},{\overline{\mathbf{G}}}_{\mathbf{c}}$, and ${\tilde{\mathbf{G}}}_{\mathbf{r}\times \mathbf{c}}$.
9.	Initialize each flux ($v$) through a two-layer perceptron which returns single cell fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$ given ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}$ as described below.
10.	Optimize fluxes to minimize the sum of the four loss terms:
	a. Metabolite accumulation in cells and TME using the stoichiometry matrix:
	$L_1={\alpha }_1\sum _c\sum _{k\in \mathit{\text{int}}.}{\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}}{\mathbf{V}}_{\mathbf{r},\mathbf{c}}\right)}^2+{\alpha }_1\sum _{k,r\in \mathit{\text{exc}}.}{\left(\sum _{ct\in \mathit{\text{sec}}.}\frac{{\sum }_c{\mathbf{V}}_{\mathbf{r},\mathbf{c}}^{\mathbf{r}\in \mathbf{s}\mathbf{e}\mathbf{c}.}}{{\sum }_{c\in ct}\mathbf{1}}-\sum _{ct\in up.}\frac{{\sum }_c{\mathbf{V}}_{\mathbf{r},\mathbf{c}}^{\mathbf{r}\in \mathbf{u}\mathbf{p}.}}{{\sum }_{c\in ct}\mathbf{1}}\right)}^2$
	Where the first term represents cellular flux balance equations for intercellular metabolites and the second term represents exchange flux balances in the TME which sets the secretion of metabolite k from sender cell types ($ct\in \mathit{\text{sec}}$.) equal to its uptake by receiver cell types ($ct\in up$.).
	b. Negative fluxes:
	$L_2={\alpha }_2\sum _c\sum _r\left(\left|{\mathbf{V}}_{\mathbf{r},\mathbf{c}}\right|-{\mathbf{V}}_{\mathbf{r},\mathbf{c}}\right)$
	c. Flux variations for cells with similar metabolic activity:
	$L_3={\alpha }_3\sum _c{\left(\sum _r{\mathbf{V}}_{\mathbf{r},\mathbf{c}}-{\overline{\mathbf{G}}}_{\mathbf{c}}\right)}^2$
	d. Isotopologue accumulation in cells:
	$L_4={\alpha }_4\sum _c\sum _k\sum _i{\left(\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}}\odot {\mathbf{M}}_{\mathbf{k},\mathbf{r}}^i\right)\left(\frac{1}{ϵ+{\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}}\odot {\mathbf{V}}_{\mathbf{r},\mathbf{c}}\right)\right)}^2$
	Since MIDs are similar across the cells in the same tissue, the ${\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}$ considers the dissimilarities between cells by adding the reaction associated gene expression information into the objective function. The element-wise inversion of ${\tilde{\mathbf{G}}}_{\mathbf{r},\mathbf{c}}$ normalized ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$ such that a reaction with a higher associated gene score carries a higher flux. We adopted this idea from COMPASS penalty score34. $ϵ$ is a small number that prevents the division by 0.
	e. Isotopologue accumulation in tissue:
	$L_5={\alpha }_5\sum _{\mathit{\text{tissue}}}\sum _i\sum _k{\left(\sum _{ct\in \mathit{\text{tissue}}}\frac{{\sum }_c\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}>0}{\mathbf{V}}_{\mathbf{r},\mathbf{c}}\prod _{\begin{array}{c}j\mid j\to k\in r\\ \mathrm{\Sigma }l=i\\ S_{j,r}<0\end{array}}{\mathrm{M}}_{\mathrm{j},\text{l}}+{\mathbf{S}}_{\mathbf{k},\mathbf{r}<\mathbf{0}}{\mathbf{V}}_{\mathbf{r},\mathbf{c}}{\mathrm{M}}_{\mathrm{k},\mathrm{i}}\right)}{{\sum }_{c\in ct}\mathbf{1}}\right)}^2$
	$L_5$ represents the isotopologue balance equations for metabolites in normal and tumor tissues. The first term describes the production of isotopologue $i$ of metabolite $\text{k}\left(M_{k,i}\right)$ from metabolites $\text{j}\left({\mathrm{M}}_{\mathrm{j}}\right)$ in reactions $r$, and the second term shows its consumption. Since enrichment data comes from bulk tissues, isotopologue balance equations are written on tissue-specific isotopologues, although fluxes are calculated for each cell. Therefore, accumulation of ${\mathrm{M}}_{\mathrm{k},\mathrm{i}}$ is averaged for each cell type and added up for cell types in the same tissue.
	Lagrange multipliers ${\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4,{\alpha }_5$ are set empirically. Optimization stops when there is no improvement observed in the total loss value and the weights of MLP become fixed.
11.	Estimate fluxes ${\mathbf{V}}_{\mathbf{r},\mathbf{c}}$: With optimized weights, MLP can estimate single cell fluxes given ${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{c}}$.

Quantification of serine-related single cell fluxes including circulating and TME exchange fluxes in our patient cohort and PDXs using scRNA-seq and bulk MIDs (¹³C-scMFA model for serine)

To understand the contribution of serine sources in glioma serine pool, we integrated glioma scRNA-seq data with cortex, glioma, and plasma MIDs. Since all three metabolic interaction analyses (MAS, MEBOCOST, modified scFEA) suggested astrocytes as a serine provider in the TME, we defined the direction of TME exchange reactions as described in Table S3. Consequently, the TME serine MIDs are assumed to match cortex MIDs because astrocytes are in tumor periphery. To generate both TME and circulating serine uptake/secretion, we assigned the transporter genes (SLCs). Since the circulating serine MIDs differ from TME serine MIDs, ¹³C-scMFA can distinguish between these two exogenous serine sources; even though their associated genes are the same. Due to limited scRNA sequencing of patient cortex samples, we assumed that the gene expression of astrocytes and neurons (cortex resident cell types) is similar among patients with glioma. The gene expression of astrocyte and neurons were borrowed from Darmanis et al.’s study. The cortex single cell fluxes will be corrected by integrating the cortex MIDs of patients, hence reducing the bias from similar gene expression assumption. The expression of serine-related genes for PDXs were extracted from the scRNA-seq data including both tumor and cortex samples. Our cell annotations show that 96.5% of astrocytes and 99.6% of neurons belong to cortex samples so we assigned cortex MIDs to astrocytes and neurons. On the other hand, 96.6% of neoplastic cells belong to tumor samples and tumor MIDs were assigned to these cells.

We assumed that unlabeled serine source comes from autophagy-related enzymes such as ULK1/2, ATG13, ATG101, RB1CC1. Since these enzymes form ULK1 complex, to integrate it into other metabolic enzymes defined in Table S3, we utilized the Boolean gene-to-reaction mapping to assign the gene expression to $SE{R}_u\to \mathit{\text{SER}}$. ULK1 and ULK2 are paralogues, hence their Boolean relationship is ULK1 OR ULK2. However, the other enzymes are subunits of ULK1 complex, and they follow AND relationship. Consequently, the whole relationship of enzymes for ULK1 complex is (ULK1 OR ULK2) AND ATG13 AND ATG101 AND RB1CC1. The Boolean expression is described by taking the sum for OR relationship and taking the minimum of imputed gene expression (step 2 of algorithm 3) for AND relationship.

Fluxes were generated through an MLP using the associated gene expression and balanced to minimize the accumulation of intra- and intercellular metabolites as well as accumulation of intracellular MIDs, and bulk MIDs. The balance equations for cellular fluxes are shown in Tables S4 and S5. Lagrange multipliers were set to 1. The same metabolic model was applied to patient samples and PDXs. Distribution of single cell fluxes were shown for each cell type. Single cell fluxes of neoplastic cells were shown based on the cell’s tissue of origin, tumor (neoplastic) or brain (invading neoplastic) in Figure 6J–M.

Quantification of purine-related single cell fluxes in our patient cohort using scRNA-seq and bulk MIDs

To understand the contribution of GMP sources including HPRT1-dependengt and IMPDH-dependent GMP routes in glioma, we integrated our glioma patient scRNA-seq data with glioma MIDs. Gene expression score for purine pathways calculated by Seurat module score to compare purine pathway scores between cell types (Figure 7B). Genes included in each score are as follows: PPAT, PAICS, PRPS1, PRPS1L1, PFAS, GART, ADSL, ATIC, PRPS2 for de novo IMP synthesis, IMPDH1, IMPDH2, GMPS for IMP → GMP, NT5C, NT5E, NT5C2, NT5M, NT5C1B, NT5C1A, NT5DC4 for nucleotide → nucleoside, PNP, LACC1 for nucleoside → nucleobase, SLC28A1, SLC28A2, SLC28A3, SLC29A1, SLC29A2, SLC29A3, SLC43A3 for nucleobase/side transporters. Due to a distinct gene expression of purine salvage pathway between myeloid and neoplastic cells and availability of scRNA-seq data for glioma samples, we chose these two cell types to deconvolute the purine de novo and salvage pathway metabolic fluxes in glioma tissues. Our purine model includes the reactions shown in Table S6. Metabolites present in this model include 6 labeled stoichiometric- and isotopic-balanced metabolites (IMP, AMP, GMP, GDP, INO, GUO), 3 unlabeled input metabolites (HPX, GUA, ADE, CO₂), and 3 labeled input metabolites (GLY, MTHF, R5P).

Fluxes were generated through an MLP using the associated gene expression and balanced to minimize the accumulation of intracellular metabolites as well as accumulation of intracellular MIDs, and bulk MIDs in glioma compartment. The balance equations for cellular fluxes are shown in Tables S7 and S8. Lagrange multipliers were set empirically to 1 for patient samples and ${\alpha }_1,{\alpha }_3$ were set to 0.1 for GBM38 and TRP. Since the enrichment data for MTHF is not available, similar to our previous approach⁹, we estimated the enrichment of methyl unit from serine and glycine enrichments at pseudo-steady state which assumes enrichments are at equilibrium at any given time.

Preprocessing of gene expression matrix (step 1 of algorithms 2 and 3)

Read counts are normalized with the scale factor of 10,000 and log2-transformed. For each cell type, a gene expression matrix is extracted given the gene names in the metabolic model and cell ids corresponding to that cell type. The cell type gene expression matrices are combined in the form of a block diagonal matrix.

Reconstruction of gene expression (step 4 of algorithms 2 and 3)

In order to generate all fluxes with the same MLP structure, the input shape has to be adjusted. Since the number of genes related to different reactions may vary, using the gene expression matrix as is might not be aligned with a fixed-structure MLP. Hence, we reconstruct gene expressions to match with the MLP input shape. To do so, first, the input block diagonal gene expression matrix is imputed using MAGIC⁶⁸. Then, a zero matrix with the shape of (number of genes × number of cell types × number of reactions, number of cells) is filled with the genes associated with each reaction.

Design of MLP (step 7 of algorithm 2 and step 9 of algorithm 3)

Flux of reaction r for cell c $\left(V_{r,c}\right)$ is defined as an MLP with one hidden layer with 8 nodes and tanhshrink activation function. Input layer of MLP is a vector of gene expression of a cell (${\mathbf{G}}_{(\mathbf{g}\times \mathbf{c}\mathbf{t}\times \mathbf{r})\times \mathbf{1}}$) and the output layer has one node which generates a flux for reaction r. Weights of $\text{MLP}\left(\mathbf{W}\right)$ are generated randomly and trained using batch gradient descent. The bias term is omitted in both hidden and output layers. In other words, each flux is described as:

$${\mathbf{V}}_{\mathbf{r}\times \mathbf{c}}={\mathbf{W}}^{\left(\mathbf{1}\right)}\left({\mathbf{W}}^{\left(\mathbf{0}\right)}\mathbf{G}-\text{tanh}\left({\mathbf{W}}^{\left(\mathbf{0}\right)}\mathbf{G}\right)\right)$$

Where $\mathbf{G}$ is the reconstructed gene expression matrix and ${\mathbf{V}}_{\mathbf{r}\times \mathbf{c}}$ is the cellular rate of reactions with the shape of the number of reactions × number of cells. ${\mathbf{W}}^{\left(\mathbf{0}\right)}$ and ${\mathbf{W}}^{\left(\mathbf{1}\right)}$ are the weights of hidden and output layers, respectively. We used PyTorch library (2.1.2+cu121) in python 3.11 for MLP design.

Optimizing weights of MLP (step 8 of algorithm 2 and step 10 of algorithm 3)

Adam optimizer with an initial learning rate of 0.008 adjusts MLP weights to minimize the total loss and estimates fluxes in each epoch. Since we consider exchange fluxes and extracellular metabolite balances, all the cells are included in one batch and a batch gradient descent was used. Optimization stops when there is no improvement observed in the total loss value by earlystopping function which monitors total loss with min_delta=1e-4 and patience=100. Learning rate decays over epochs by ReduceLROnPlateau function with mode=‘min’, factor=0.9, patience=10, threshold=0.001, min_lr=0.001, and cooldown=10.

Isotopologue balance matrix (step 10d of algorithm 3)

¹³C-scMFA requires an isotopologue balance matrix with the shape of number of MIDs × number of reactions as an input. Considering the MID balance equations for metabolite k, this matrix is the coefficients of ${\mathbf{V}}_{\mathbf{r}}$ in the following equation.

$$\sum _r\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}>\mathbf{0}}\left(\prod _{\begin{array}{c}j\mid j\to k\in r\\ \sum l=i\\ S_{j,r}<0\end{array}}{\mathbf{M}}_{\mathbf{j},\mathbf{l}}\right){\mathbf{V}}_{\mathbf{r}}+{\mathbf{S}}_{\mathbf{k},\mathbf{r}<\mathbf{0}}{\mathbf{M}}_{\mathbf{k},\mathbf{i}}{\mathbf{V}}_{\mathbf{r}}\right)=0$$

Where r is the set of reactions that produce/consume metabolite k. ${\mathbf{S}}_{\mathbf{k},\mathbf{r}}$ is the stoichiometry coefficient of metabolite k in reaction r. The first term describes the production of isotopologue i of metabolite $\mathrm{k}\left({\mathbf{M}}_{\mathbf{k},\mathbf{i}}\right)$ from metabolites $\mathrm{j}\left({\mathbf{M}}_{\mathrm{j},\mathrm{l}}\right)$ in reactions $r$, and the second term shows consumption of ${\mathbf{M}}_{\mathbf{k},\mathbf{i}}$.

Simulation of fluxes and MIDs

To generate training data for our machine learning framework that can predict flux ratios, we simulated 50,000 sets of balanced fluxes. We empirically chose flux boundaries to generate random fluxes within the bounds (${\mathbf{V}}^{\mathbf{0}}$) and initialize an FBA-based approach to balance fluxes. We went through a series of trials to set the flux boundaries until we achieved a set of flux bounds that can generate MIDs analogous to our patient MIDs. Considering reactions in our metabolic model, fluxes are balanced (${\mathit{V}}^{\mathbf{\text{balanced}}}$) by FBA given their stoichiometric coefficients ($\mathbf{S}$) within the flux bounds (Eq. 1). Fluxes -parameters of FBA- are optimized by minimizing the following objective function:

$$\begin{gathered} {\mathbf{V}}^{\mathbf{\text{balanced}}}≔\text{min}{\sum }_{i=1}^r{\left(\mathbf{1}-\frac{{\mathrm{V}}_{\mathrm{i}}}{{\mathrm{V}}_{\mathrm{i}}^0}\right)}^2 \\ \mathrm{s}.\mathrm{t}. \end{gathered}$$ (Equation 1)

$$\begin{gathered} S.V=\mathbf{0} \\ A.V=\mathbf{0} \\ lb\le V_{\text{i}}\le ub \end{gathered}$$

Where $r$ is the number of reactions. $lb$ and $ub$ are lower bounds and upper bounds of fluxes. Since we aim to predict relative fluxes, it would be better for a machine learning model to observe various contributions of metabolite sources with the same frequency, so it is not biased toward one metabolite source. To do this, we added the second constraint ($\mathbf{A}.\mathbf{V}=\mathbf{0}$) to our optimization, where $\mathbf{A}$ constrains the relative fluxes to follow a uniform distribution (please see its definition in serine and purine models). This optimization was solved to simulate fluxes using fmincon function of MATLAB R2021b.

Our mouse multi-timepoint experiment showed tissue serine and purine MIDs do not reach at steady state during 4 hours of infusion⁹. We assumed that this is also the case in human patients who are infused with [U¹³C]-glucose during the time of craniotomy which usually takes between 2 to 4 hours. Hence, to simulate patient MIDs, we need to consider time variant MIDs for 4-hour infusion. To do so, we used an INST-MFA (isotopic nonsteady state metabolic flux analysis) model which assumes MIDs are time-dependent, but fluxes and metabolite concentrations are at steady state. In our previous study⁹, we used a dynamic MFA model to estimate fluxes in GBM PDXs with radiation treatment which is known to change metabolic reaction rates and thus, fluxes and concentrations are also time dependent. However, assumptions of INST-MFA are valid for our patient data because patients did not receive any treatment before surgery.

To perform INST-MFA, a system of ordinary differential equations (ODEs) is solved where each ODE (Eq. 2) represents the rate of change of an isopotopomer/isotopologue of a balanced metabolite. Simulated balanced fluxes are then used in ODEs to solve for isotopomer i of metabolite k (m_k,i) if there are cleavage reactions in our model:

$$\frac{{\mathrm{d}\mathrm{m}}_{\mathrm{k},\mathrm{i}}}{\mathrm{d}\mathrm{t}}=\frac{1}{{\mathrm{C}}_{\mathrm{k}}}\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}}{\mathbf{V}}_{\mathbf{r}}\prod _{\begin{array}{c}l\mid l\to k\in r\\ S_{l,r}<0\end{array}}{\mathrm{m}}_{\mathrm{l},\mathrm{j}}{\mathbf{I}\mathbf{M}\mathbf{M}}_{\mathbf{j}\to \mathbf{i}}+{\mathbf{S}}_{\mathbf{k},\mathbf{r}<\mathbf{0}}{\mathbf{V}}_{\mathbf{r}}\cdot {\mathrm{m}}_{\mathrm{k},\mathrm{i}}\right)$$ (Equation 2)

Where ${\text{C}}_{\text{k}}$ is the concentration of metabolite k, m_l,j represents isotopomers of metabolite l that produces metabolite k. ${\mathbf{I}\mathbf{M}\mathbf{M}}_{\mathbf{j}\to \mathbf{i}}$ is the isotopomer mapping matrix which maps isotopomer j to isotopomer i⁹⁹.

If all the reactions in the model are condensation reactions, we can reduce the number of parameters in the above system of ODEs from number of isotopomers $O\left(2^{i}k\right)$ to number of isotopologues $O\left(ik\right)$. Hence the system of ODEs is defined as follows (Eq. 3).

$$\frac{{\mathrm{d}\mathrm{M}}_{\mathrm{k},\mathrm{i}}}{\mathrm{d}\mathrm{t}}=\frac{1}{{\mathrm{C}}_{\mathrm{k}}}\left({\mathbf{S}}_{\mathbf{k},\mathbf{r}}{\mathbf{V}}_{\mathbf{r}}\prod _{\begin{array}{c}j\mid j\to k\in r\\ \sum l=i\\ S_{j,r}<0\end{array}}{\mathrm{M}}_{\mathrm{j},\mathrm{l}}+{\mathbf{S}}_{\mathbf{k},\mathbf{r}<\mathbf{0}}{\mathbf{V}}_{\mathbf{r}}.{\mathrm{M}}_{\mathrm{k},\mathrm{i}}\right)$$ (Equation 3)

The solver ode23s was used to solve the system of ODEs as an initial value problem. Initial guess was set to a vector with the length of balanced metabolite isotopomers/isotopologues as they are all unlabeled at time 0. We set a time difference of 0.1 hour ($\Delta t$) to calculate the rate of isotopomer/isotopologue changes.

Simulation of serine fluxes

We considered fluxes in both cortex and glioma including glucose-derived (de novo) serine synthesis, plasma serine uptake, unlabeled serine sources (originated from autophagy and protein degradation) as serine sources and serine-derived glycine formation and serine consumption excluding glycine formation (i.e., serine sink flux or $\mathit{\text{SER}}\to SE{R}_{\mathit{\text{out}}}$) as serine consumption fluxes. In addition, we included glycine cleavage flux and sink fluxes of glycine and MTHF which balance metabolites within the boundaries of our metabolic model. Our modified scFEA approach suggested there is a net uptake flux for neoplastic cells form the TME, hence, for glioma compartment, we also added a TME serine uptake flux $\left(SE{R}_c\to SE{R}_g\right)$. Serine-related reactions and flux bounds are shown in Table S9.

To predict relative fluxes of serine sources in glioma and cortex, we generated the target fluxes (i.e., serine sources fluxes) with a uniform distribution. To align the generation of fluxes with our CNN model output, we ran the optimization three times, each time matrix $\mathbf{A}$ in Eq. 1 was changed based on the target flux. For example, to predict glucose-derived serine relative to total serine sources, elements of ${\mathbf{A}}_1$ that are multiplied to fluxes of $P{G}_g\to SE{R}_g$, $SE{R}_p\to SE{R}_g$, and $SE{R}_c\to SE{R}_g$ are set to the first following equation (Eq. 4-1) and other elements are set to 0. This is similar for prediction of relative flux of $SE{R}_p\to SE{R}_g$ (Eq. 4-2) or $P{G}_c\to SE{R}_c$ (Eq. 4-3).

$$\begin{gathered} 1.A_{1,P{G}_g\to SE{R}_g}=1,A_{1,SE{R}_p\to SE{R}_g}=\frac{y_1}{y_1-1},A_{1,SE{R}_c\to SE{R}_g}=\frac{y_1}{y_1-1},y_1=\frac{P{G}_g\to SE{R}_g}{P{G}_g\to SE{R}_g+SE{R}_p\to SE{R}_g+SE{R}_c\to SE{R}_g} \\ 2.A_{2,SE{R}_p\to SE{R}_g}=1,A_{2,P{G}_g\to SE{R}_g}=\frac{y_2}{y_2-1},A_{2,SE{R}_c\to SE{R}_g}=\frac{y_2}{y_2-1},y_2=\frac{SE{R}_p\to SE{R}_g}{P{G}_g\to SE{R}_g+SE{R}_p\to SE{R}_g+SE{R}_c\to SE{R}_g} \\ 3.A_{3,P{G}_c\to SE{R}_c}=1,A_{3,SE{R}_p\to SE{R}_c}=\frac{y_3}{y_3-1},y_3=\frac{P{G}_c\to SE{R}_c}{P{G}_c\to SE{R}_c+SE{R}_p\to SE{R}_c} \end{gathered}$$ (Equation 4)

Where $y^{\left(k\right)}≔a+k\left(\frac{b-a}{n-1}\right)|k=\mathrm{0,1},\dots ,n-1$ is a linearly spaced vector of $n$ values between $a$ and $b$. Based on the above definition, $y$ is in the range of [0, 1]. Here, we set $a=0.01$, $b=0.99$ and $n=100$. $y$ is repeated 500 times and shuffled to be assigned to 50,000 number of simulations.

Simulation of MIDs for serine model

To perform INST-MFA for serine model, a system of ODEs is solved where each ODE represents the rate of change of an isopotopomer of a balanced metabolite. These equations cannot be written on isotopologues because some reactions in serine model are cleavage reactions and considering atom transition is necessary (Table S9). Input metabolites of serine model include unlabeled serine and ¹³C-labeled metabolites (i.e., ${PG}_g,P{G}_c,SE{R}_p$). For ¹³C-labeled input metabolites, we defined a range of possible MIDs based on our patient MIDs (Table S10). These bounds are then assigned to certain isotopomers. Based on our findings from our previous study⁹, we assumed that isotopomers of input metabolites are more abundant in the form of 001 (among 100, 010, 001 for M+1 isotopologues) and 110 (among 110, 101, 011 for M+2 isotopologues) and the defined MID bounds are set to these isotopomers for input metabolites. These assumptions are verified if the simulated MIDs are in the range of patient MIDs. In the system of ODEs, only isotopomers of balanced metabolites are parameters and fluxes and concentrations are hyper parameters as described before. To simulate isotopmers of balanced metabolites, we solved the system of ODEs shown in Eq. 2. Finally, the simulated isotopomers are mapped to isotopologue distributions.

Simulation of purine fluxes

Our purine model only includes glioma fluxes because enrichment of purines in cortex is very low. This model includes de novo synthesis of nucleotides as well as salvage of nucleobases to produce nucleotides. Purine-related reactions and flux bounds are shown in Table S11. To predict relative fluxes of GMP sources in glioma, we generated the target fluxes (i.e., IMPDH-dependent GMP synthesis and salvage GMP synthesis) with a uniform distribution. Matrix $\mathbf{\text{A}}$ in objective function (Eq. 1) for purine model is set to the following coefficients for IMPDH-dependent and salvage GMP synthesis and other elements of $\mathbf{\text{A}}$ are set to 0.

$$A_{\mathit{\text{IMP}}\to \mathit{\text{GMP}}}=1,A_{\mathit{\text{GUA}}+R5P\to \mathit{\text{GMP}}}=\frac{y}{y-1},y=\frac{\mathit{\text{IMP}}\to \mathit{\text{GMP}}}{\mathit{\text{IMP}}\to \mathit{\text{GMP}}+\mathit{\text{GUA}}+R5P\to \mathit{\text{GMP}}}$$ (Equation 5)

Where $y^{\left(k\right)}≔\left.a+k\left(\frac{b-a}{n-1}\right)\right|k=\mathrm{0,1},\dots ,n-1$ is a linearly spaced vector of $n$ values between $a$ and $b$.

Based on the above definition, $y$ is in the range of [0, 1]. Here, we set $a=0.01$, $b=0.99$ and $n=100.y$ is repeated 500 times and shuffled to be assigned to 50,000 number of simulations.

Simulation of MIDs for purine model

To perform INST-MFA for purine model, a system of ODEs is solved where each ODE represents the rate of change of an isotopologues of a balanced metabolite. Reactions in purine model are condensation reactions, so MIDs can be simulated by Eq. 3. Input metabolites of purine model include unlabeled sources (i.e., HPX, GUA, ADE, CO₂) and ¹³C-labeled metabolites (i.e., SER, R5P). For ¹³C-labeled input metabolites, we defined a range of possible MIDs based on our patient MIDs (Table S12). These bounds are verified if the simulated MIDs are in the range of patient MIDs. In the system of ODEs, only MIDs of balanced metabolites are parameters and fluxes and concentrations are hyperparameters.

Evaluation of simulated MIDs

To investigate whether simulated MIDs resemble patient MIDs, ranges of simulated MIDs were compared to patient MIDs. In addition, simulated MIDs (in 2–4hr) of metabolites used in CNN were combined with 100 samples per patient tissue drawn from a truncated normal distribution with mean and standard deviation of patient ¹³C-fractional MIDs. Simulated and patient MIDs were scaled. All features (i.e., MIDs) were used in principal component analysis. The first 5 PCs were used to find neighbors, clusters (with resolution = 0.1), and run t-SNE. We used simulated MIDs in the CNN if the range of simulated MIDs includes range of patient MIDs and patient MIDs overlap with simulated MIDs in the t-SNE space. Features for serine t-SNE projection include MIDs (M+0 to M+3) of SERg, PGg, SERp, SERc, and PGc. Features for purine t-SNE projection include MIDs (M+0 to M+5) of IMP, GMP, GDP, GUO, INO, AMP, R5P and M+0 to M+3 of serine.

Metabolic CNN

Here, we implemented a convolutional neural network model to predict the contribution of fluxes that produce a metabolite. We utilized FBA and mass isotopomer/isotopologue balances at nonsteady state to simulate thousands of instances of synthetic patient data which is then fed into a convolutional neural network (CNN) framework as input features. The target values or predictions are relative values of fluxes that produce a metabolite (metabolite Z) from various sources (metabolites W, X, Y) (Figure 1). These relative values are calculated from FBA and used as ground truth values in a supervised manner. CNN learns how these relative fluxes change by changing metabolites enrichments at various time points. After the CNN is trained, it can predict the relative anabolic fluxes from MIDs.

Prepare simulated data for CNN

MIDs of balanced and input labeled metabolites are imported as well as anabolic fluxes of target metabolite Z. In each simulation, we considered the ratio of one target anabolic flux to all anabolic fluxes has a uniform distribution. CNN was trained on each simulation to predict these relative fluxes from simulated MIDs. Due to patient and mouse infusion time, a subset of MIDs from 2 to 4 hrs was selected to train the CNN (features). Since $\Delta t$ in simulation was set to 0.1 hr, for each set of simulated fluxes, there are 21 timepoints for MIDs (at 2, 2.1, 2.2, …, 4 hr). The original simulated data was stored as a matrix with rows representing flux set index and time point and columns representing MIDs of related metabolites. The target values of CNNs denoted by $y$ in simulation section are concatenated to simulated MIDs and shuffled by simulated flux indices. Then, the simulated data is split into 68% training, 17% validation, and 15% test datasets. To scale data by simulation instances (i.e., number of flux sets), training data is reshaped to (flux sets, time points × number of metabolites × number of MIDs) and mean and standard deviation of training MIDs are calculated by fit function of StandardScalar in sklearn package. The scalar is then used to transform training, validation, and test datasets by removing the mean and scaling to unit variance. Furthermore, simulated MIDs of all datasets were reshaped to a 4-dimensional matrix with the shape of (number of flux sets in each data set × no. of simulated timepoints, number of metabolites, number of isotopologues, 1) to be aligned with CNN input layer.

Prepare simulated data for CNN input layer for serine and purine models

Input features of serine model include MIDs (fractional enrichment of M+1 to M+3) of serine (SERg) and phosphoglycerate (PGg) in glioma compartment, plasma serine (SERp), and serine (SERc) and phosphoglycerate (PGc) in cortex compartment. We ran three simulations (Eq. 4) to generate relative fluxes of glucose-derived serine synthesis and plasma serine uptake in glioma and glucose-derived serine synthesis in cortex. Since serine sources in glioma and cortex sum to 1 in simulations (Eq. 4), the TME-derived serine uptake flux in glioma and plasma serine uptake flux in cortex are calculated from CNN predicted glucose-derived serine and plasma serine uptake in glioma and glucose-derived serine in cortex. Input features of purine model include MIDs (fractional enrichment of M+1 to M+5) of inosine monophosphate (IMP), guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine (GUO), inosine (INO), adenosine monophosphate (AMP), ribose 5-phosphate (R5P), and serine (SER) in glioma compartment. Since input layer of CNN is in 2-dimensional form, all metabolites need to have the same number of MIDs. To adjust this for serine MIDs in purine model, we added hypothetical M+4 and M+5 serine to the data and set them to 0. We ran one simulation (Eq. 5) to generate relative fluxes of IMPDH-dependent GMP synthesis in glioma. Since GMP sources in glioma sum to 1 in simulations (Eq. 5), the salvage GMP flux in glioma is calculated from CNN predicted IMPDH-dependent GMP synthesis in glioma.

Implementation of CNN

The input layer of CNN is configured based on the shape of our input data to (number of metabolites, number of isotopologues, 1). The input layer is followed by a two-dimensional convolution layer (Conv2D) with a kernel size of (number of metabolites, 1). Number of filters of Conv2D layer is set to 24 which results in an output space of (1, number of isotopologues, number of filters) tensors. A one-dimensional convolution layer (Conv1D) is applied to the Conv2D output with a kernel size if (number of isotopologues,) and number of filters = 40. Output of Conv1D is then flattened and enters a fully connected neural network with two dense layers with 32 and 16 neurons, respectively. Finally, the output layer is a dense layer with 1 neuron which estimates a relative flux. The intuition behind this network is that the Conv2D kernel applies on one isotopologue of all metabolites at a time which then captures the dependencies between different metabolites with the same MIDs similar to writing a mass isotopologue balance. The Conv1D kernel applies on all isotopologues which can capture the total enrichment. The bias term for all learnable layers is set to 0. After each learnable layer, ReLU activation function and batch normalization are applied except for the output layer which has a sigmoid activation function to ensure the relative flux is between 0 and 1.

To train the CNN, the trainable parameters such as the weights of layers must be optimized such that a loss function is minimized. A convolution layer consists of a kernel with trainable weights that cross-correlate to its previous layer output. Weights of all layers are initialized by He uniform variance scaling function. A mini batch gradient descent approach with the size of 256 was selected to update all the weights according to the gradient of loss function using Adam optimizer with learning rate of 0.004 and epsilon of 0.4. Since a relative flux value is a continuous variable, a regression model is required to predict it. Hence, we set the loss function to the mean squared error (MSE). Training stops by early stopping function when there is no improvement observed in the loss value of validation data with min_delta=1e-6 and patience=8. Learning rate decays over epochs if there is no improvement in validation loss by ReduceLROnPlateau function with factor=0.9, patience=5, min_lr=0.001. We utilized these functions from the TensorFlow (Keras) library (v2.10.1) in python 3.8.

CNN hyperparameter optimization

We used Bayesian optimization to tune hyperparameters of CNN model including number of Dense layers in fully connected network, number of neurons in each Dense layer, Adam optimizer hyperparameters learning rate and epsilon. To perform hyperparameter optimization, we used Optuna library in Python 3.8. An Optuna object first samples randomly from different choices of combinations of hyperparameters. Optuna then utilizes a surrogate function such as Tree Parzen Estimator (TPE sampler) to efficiently search for the best hyperparameters in 50 combinations of hyperparameters. During different trials of hyperparameters, the CNN model is trained and evaluated on validation data. The objective function for Optuna is to maximize the coefficient of determination of target and predicted values for validation dataset. The range of sampling for hyperparameters are as follows:

• Learning rate (hyperparameter of Adam optimizer) from 0.001 to 0.01 in log scale

• Epsilon (hyperparameter of Adam optimizer) from 0.001 to 1 in log scale.

• Number of neurons in Dense layers from 15 to 40

• Number of Dense layers from 1 to 5

Based on Optuna’s trials, we selected 2 Dense layers with 32 and 16 neurons, learning rate=0.004 and epsilon=0.4.

Preparation of patient and mouse MIDs as input of CNN

Since the technical variations of measured percent enrichment of metabolites in patients and mice were relatively high, we calculated the mean and standard deviation of technical replicates for each biological sample. 100 samples were drawn from a truncated normal distribution with the same mean and standard deviation and between 0 and 1. The unlabeled isotopologue M+0 was set such that sum of MIDs equals 1. These samples were used as input of CNN to increase the confidence of the predictions. The standard scalar was fitted on the training data and can be used to transform patient and mouse MIDs. The time of infusion for each patient and mouse is known and MIDs can be scaled by mean and standard deviation of training MIDs at the same timepoint. Scaled patient and mouse MIDs are reshaped to align with the input layer of CNN and the CNN predicts the relative flux in patients and mice. MIDs of purines are imputed to reduce noise for both mice and patients.

Imputation of MIDs

Due to a high technical variation in percent enrichment and relatively low percent enrichment of purine metabolites, we imputed MIDs used in purine model. We borrowed a data imputation approach from Wang et al.¹⁰⁰ to lower technical variations in purine model MIDs. To do so, we simulated 10,000 flux sets and their corresponding MIDs separate from training data simulation. Unlabeled isotopologues were removed from simulated and experimental MIDs. Simulated MIDs in 2 to 4 hr infusion time were selected to align with patient infusion times. The percent enrichment of purine model metabolites for simulated, patient, and mouse MIDs was normalized and scaled using SCTransform function of Seurat (v4.2.0) and principal component analysis was performed on scaled data. RunUMAP with number of neighbors = 30 was performed on the simulated MIDs. To align experimental MIDs to simulated MIDs, simulated MIDs were set as reference dataset and experimental MIDs were set as query dataset. Seurat anchors were found and used to transfer data from the simulated MIDs to experimental MIDs.

Metabolic flux analysis informed by CNN predicted relative fluxes

We adopted a similar approach to our previous study⁹, to quantify serine fluxes in cortex and glioma with the difference of adding a TME-derived serine source for the glioma. This approach was used to evaluate CNN by back calculation of MIDs from CNN predicted fluxes and comparing them with experimental MIDs. In addition, we are able to compare serine fluxes between two compartments. Since CNN predicts fluxes relatively in each compartment, comparing a similar flux but from two compartments is not possible. In CNN and in our previous MFA model⁹, fluxes of serine sources were added to 1 in each compartment, hence comparing fluxes in the same compartment was achievable. For example, we observed cortex has a higher de novo synthesis flux than plasma uptake flux. However, from the previous analysis, one cannot conclude whether de novo synthesis flux is higher in cortex or glioma. It is good to note that an MFA alone is highly underdetermined, and many solutions are possible. In addition, MFA assumes isotopic steady state opposed to CNN framework.

The MFA informed by CNN model comprises two compartments cortex and glioma. Reactions used in MFA model are similar to serine simulation model (Table S9). Both compartments have their own PG pool to synthesize serine de novo. A circulating serine pool is also available for both compartments. Based on our modified scFEA analysis which shows there is a net flux from cortex to glioma, we also added a TME-derived serine pool for glioma compartment. An unlabeled serine source was also added to both compartments to include serine sources from protein breakdown and autophagy^43,101. Since serine model includes cleavage reactions, MFA balance equations are written on isotopomers which results in introducing more variables than equations. To reduce the model uncertainty, we added 4 linear constraints:

• Fluxes of serine sources in glioma are set to CNN predicted relative fluxes (sum of serine sources equals 1). This adds 3 linear equality constraints for de novo serine synthesis, plasma serine uptake, and TME-derived serine uptake.

• Ratio of de novo serine synthesis to total serine synthesis in cortex is set to CNN prediction. This adds 1 linear equality constraint.

Model parameters consist of fluxes and isotopomers of plasma serine and PG, serine, glycine, and MTHF in glioma and cortex. For the metabolites inside the compartments, we balanced fluxes by stoichiometry coefficients assuming that fluxes are at steady state. Isotopomers of metabolites inside the compartments are also balanced, assuming that they are at steady state. The model parameters are initialized randomly 10 times within the range of 0 and 1. We set the initial values of unlabeled serine uptake fluxes to 0 to prevent overestimation of unlabeled pools. Parameters are optimized to minimize the differences between experimentally measured MIDs and MIDs estimated by MFA as described below.

$$\begin{gathered} \text{min}\sum _M{\left(\frac{{\sum }_m\text{IDV}-{\text{MID}}_{\text{exp}}}{{\text{SD}}_{\text{exp}}}\right)}^2 \\ \text{s.t.} \end{gathered}$$

$$\begin{gathered} S.V=\mathbf{0} \\ A.V=\mathbf{0} \\ {\sum }_{m\in M}\text{IDV}=1 \\ {S}_{k,r}{V}_r\prod _{\begin{array}{c}l\mid l\to k\in r\\ S_{l,r}<0\end{array}}{\text{IDV}}_{\text{l},\text{j}}IM{M}_{j\to i}+S_{k,r<\mathbf{0}}{V}_r.{\text{IDV}}_{\text{k},\text{i}}=\mathbf{0} \\ lb\le \left[\text{V},\text{IDV}\right]\le ub \end{gathered}$$

Where $\mathbf{V}$ and $\mathbf{I}\mathbf{D}\mathbf{V}$ represent parameters of MFA, fluxes and isotopomer distribution, respectively. $m$ and $M$ denote number of isotopomers and isotopologues, respectively. MID_exp and SD_exp are experimental MIDs and their corresponding standard deviation. The first linear constraint represents flux balance equations governed by the stoichiometric coefficients. The second linear constraint sets relative fluxes of serine in glioma and cortex based on CNN predictions (denoted as $y$ in simulation of serine model (Eq. 4)). The third linear constraint shows sum of isotopomer of a metabolite equals 1. The fourth nonlinear equality constraint represents isotopomer balance equations. The fifth linear inequality constraint sets lower and upper bounds for model parameters. Lower bounds for fluxes and IDVs were set to 0.01, 1e-7, respectively. Upper bounds for fluxes and IDVs were set to 20 and 1. To solve this optimization problem, we used Artelys Knitro software (v12.4) in MATLAB R2021b. To estimate 95% confidence intervals of model parameters, we sampled 100 times from experimental MIDs assuming the noise in MIDs follows a truncated normal distribution with mean and standard deviation of experimental MIDs. Then we ran optimization 100 times with initial guesses set to parameters of the optimization with lowest objective value and estimated the change in model parameters when a gaussian noise is added to the experimental MIDs.

Linear regression analysis for fractional contribution estimation of de novo and salvage GMP synthesis

To deconvolute the contributions of IMPDH-dependent and HPRT1-dependent GMP synthesis flux using co-administration of [U¹³C]-glucose and [U¹³C]-serine tracers, a linear regression model was used²³. To create this model, the number of carbons must be the same between a substrate and a product. Otherwise, hypothetical MIDs can be calculated for a product if a substrate is the only contributor to product labeling¹⁰². Since HPRT1-dependent GMP synthesis is a concentration reaction that combines PRPP with guanine, we calculated hypothetical MIDs (Y) of the combined salvage substrates as follows:

$${\mathrm{Y}}_{\mathrm{M}+\mathrm{k}}=\sum _{\begin{array}{c}i,j\in \mathrm{0,1},\dots ,5\\ i+j=k\end{array}}{\mathrm{G}\mathrm{U}\mathrm{A}}_{\mathrm{M}+\mathrm{i}}\cdot \mathrm{R}5{\mathrm{P}}_{\mathrm{M}+\mathrm{j}}$$

Where GUA_M+i and R5P_M+j are guanine and R5P experimental MIDs (M+0-M+5) and Y_M+k is the hypothetical MIDs of GMP (M+0-M+10) if GMP is only labeled from salvage pathway. Then, the linear regression model estimates GMP MIDs based on the hypothetical MIDs of salvage pathway (Y), experimental MIDs of IMP, and fractional contribution of de novo and salvage pathways (Eq. 6). Sum of the fractional contribution of de novo and salvage pathways is 1, thus there is only one variable in this model ($F_{\mathit{\text{de}}\mathit{\text{novo}}}$). The model minimizes the sum of squares of experimental GMP MIDs and estimated GMP MIDs by optimizing the de novo fractional contribution (Eq. 7). This analysis is shown in Data S1.

$${\text{GMP}}_{\mathrm{M}+\mathrm{k}}^{\text{est.}}=F_{\mathit{\text{de}}\mathit{\text{novo}}}\cdot {\text{IMP}}_{\mathrm{M}+\mathrm{k}}^{\text{exp.}}+\left(1-F_{\mathit{\text{de}}\mathit{\text{novo}}}\right)\cdot {\mathrm{Y}}_{\mathrm{M}+\mathrm{k}}$$ (Equation 6)

$$\text{min}{\sum }_{k=1}^{10}{\left({\text{GMP}}_{\mathrm{M}+\mathrm{k}}^{\text{est.}}-{\text{G}}_{\mathrm{M}+\mathrm{k}}^{\text{exp.}}\right)}^2$$ (Equation 7)

Quantification and statistical analysis

Statistical analyses were performed using R 4.2.2, GraphPad Prism 10, and Python 3.8. MEBOCOST determined the statistical significance of communication scores by performing a one-tailed permutation test, in which cell IDs were randomly shuffled across all cells in the scRNA-seq data. The p-values were corrected using Benjamini-Hochberg method to control the false discovery rate (FDR<0.05). Number of datapoints per group for CNN-predicted fluxes and informed MFA-estimated fluxes is 100. Wilcoxon rank-sum test corrected by Holm–Bonferroni method was used to compare distribution of CNN-predicted relative fluxes and single-cell fluxes. One-way ANOVA with Benjamini and Hochberg correction (FDR=0.001) was used to assess CNN-predicted fluxes in control vs. MMF-treated mice; Mann-Whitney tests were used to compare CNN-predicted fluxes in GBM38 vs TRP tumors. Experimental data were assessed using unpaired two-sided t-test with Welch’s correction. Groups contained 1–3 technical replicates of 2–4 biological replicates per group. In correlation plots, a linear model was fitted to data; confidence bands represent 95% confidence intervals, and plots report Pearson’s r and p-value. In box plots, center line represents median, box limits represent upper and lower quartiles, and whiskers show 1.5x interquartile range. Outlier points are hidden. Violin plots were trimmed to the range of the data. All violins have the same maximum width. Bar plots represent mean ± standard deviation. Statistical methods are described in detail in the figure legends.

Supplementary Material

1

Data S1. Unprocessed source data underlying all graphs, related to Figures 2–7 and S2–S7.

2

Document S1. Figures S1–S7, Tables S1–S12, and supplemental references.

Highlights.

• Digital twin framework (DTF) quantifies metabolic fluxes in human tumors.

• DTF estimates single-cell fluxes within the TME.

• DTF determines which patients may benefit from a serine/glycine-free diet.

• DTF identifies which patients may benefit from pharmacological nucleotide targeting.