Method for assessing metabolic flux

Abstract

The present disclosure relates to methods for assessing metabolic flux. In some aspects, the disclosure relates to a method for estimating the absolute metabolic flux of a pathway of interest based on the level of one or more metabolites and / or isotopic bodies thereof at a single point in time after administration of a tracer to a subject. In some embodiments, the methods described herein are performed or generated using an artificial intelligence / machine learning (AI / ML) model.

Description

[0001] Priority Claim

[0002] This application claims priority to U.S. Provisional Application No. 63 / 416,146, filed on Oct. 14, 2022, the entire content of which is incorporated herein by reference. Technical Field

[0003] The present disclosure relates to methods for assessing metabolic fluxes. In some aspects, provided herein is a method for estimating the absolute metabolic flux of a pathway of interest based on the levels of one or more metabolites and / or their isotopologues at a single time point after administration of a tracer to a subject. In some embodiments, the methods described herein are performed or generated using an artificial intelligence / machine learning (AI / ML) model. Background Art

[0004] Knowledge of metabolic rates in metabolic networks provides insights into the regulation of metabolism and the contribution of metabolic changes to pathology. However, there are several challenges in in vivo flux quantification: (1) metabolite uptake and secretion fluxes (i.e., exchange fluxes) cannot be experimentally measured, (2) in vivo experiments require substantial resources and can only be performed for a few hours, which is insufficient to reach isotopic steady state, and (3) inter-organ metabolism leads to secondary enrichment of circulating metabolites. Thus, there is a need for improved methods for fully assessing metabolic fluxes. Summary of the Invention

[0005] In some aspects, provided herein are methods for estimating the absolute metabolic flux of a pathway of interest. In some embodiments, the method for estimating the absolute metabolic flux of a metabolic pathway of interest comprises administering a tracer to a subject, collecting a sample from the subject, and generating an estimate of the absolute metabolic flux of the pathway of interest. In some embodiments, the sample is a tissue sample. In some embodiments, the estimate of the absolute metabolic flux of the pathway of interest is generated based on the levels of one or more metabolites and / or their isotopologues in the sample at a single time point after administration of the tracer to the subject.

[0006] In some embodiments, the pathway of interest is the purine synthesis pathway. In some embodiments, the pathway of interest is the purine synthesis pathway, and one or more metabolites and / or their isotopologues include one or more of the following: ribose-5-phosphate (R5P), glycine (GLY), carbon dioxide (CO2), 5-methyltetrahydrofolate (C-THF), inosine monophosphate (IMP), inosine, hypoxanthine, guanine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine, adenosine monophosphate (AMP), and adenosine. In some embodiments, the method further includes determining the contributing fraction of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway.

[0007] In some embodiments, the pathway of interest is the pyrimidine synthesis pathway. In some embodiments, the pathway of interest is the pyrimidine synthesis pathway, and the one or more metabolites and / or their isotopologues include one or more of ribose-5-phosphate (R5P), aspartic acid (ASP), carbon dioxide (CO2), uridine, and uridine monophosphate (UMP).

[0008] In some embodiments, the pathway of interest is the serine synthesis pathway (e.g., de novo serine synthesis pathway). In some embodiments, the pathway of interest is the serine synthesis pathway, and the one or more metabolites and / or their isotopologues include one or more of 3-phosphoglycerate (3PG), glycine (gly), and 5,10-methylene THF (Me-THF).

[0009] In some embodiments, the subject has cancer and the tissue sample includes a tumor tissue sample. In some embodiments, the estimated result of the absolute metabolic flux of the pathway of interest is generated based on the levels of one or more metabolites and / or their isotopologues in a sample at a single time point after administering radiotherapy to the subject.

[0010] In some embodiments, the estimated result of the absolute metabolic flux of the pathway of interest is generated using an artificial intelligence / machine learning (AI / ML) model.

[0011] In some embodiments, the tracer includes a moiety labeled with 13 C, 15 N, 18 O, or 2 D. In some embodiments, the moiety includes glucose, methionine, serine, glutamine, lactate, acetate, hypoxanthine, or uridine.

[0012] In some aspects, the present disclosure provides methods for selecting a therapy for a subject in need thereof. In some embodiments, a method for selecting a therapy for a subject in need thereof includes generating an estimate of the absolute metabolic flux of a pathway of interest using the methods described herein, and selecting a therapy for the subject in need thereof based on the estimate of the absolute metabolic flux of the pathway of interest. In some embodiments, the subject has cancer, and wherein the pathway of interest is a cancer-related pathway. In some embodiments, the method further includes the step of administering the selected therapy to the subject. For example, the method may further include administering a selected anti-cancer therapy to the subject based on the estimate of the absolute metabolic flux of the pathway of interest in a sample obtained from the subject.

[0013] In some aspects, the present disclosure provides machine learning methods for estimating the absolute activity of one or more metabolic fluxes. In some embodiments, a machine learning method for estimating the absolute activity of one or more metabolic fluxes includes obtaining a plurality of measurements from a sample collected from a subject, and applying an artificial intelligence / machine learning (AI / ML) model to the measurements to generate an estimate of the absolute activity of one or more metabolic fluxes. In some embodiments, each measurement is the level of a metabolite and / or its isotopologues in a metabolic pathway of interest at a single time point.

[0014] In some embodiments, the sample includes a tissue sample. In some embodiments, the subject is diagnosed with cancer or at risk of developing cancer. In some embodiments, the subject is diagnosed with cancer or at risk of developing cancer, and the tissue sample is a tumor tissue sample. In some embodiments, the plurality of measurements are obtained from the sample after administering radiotherapy to the subject.

[0015] In some embodiments, the plurality of measurements are obtained from the sample after administering a tracer to the subject. In some embodiments, the tracer includes a moiety labeled with 13 C, 15 N, 18 O or 2 D. In some embodiments, the moiety includes glucose, methionine, serine, glutamine, lactate, acetate, hypoxanthine, or uridine.

[0016] In some aspects, the present disclosure provides methods for selecting a therapy for a subject in need thereof, including estimating the absolute activity of one or more metabolic fluxes by the methods described herein and selecting a therapy for the subject in need thereof based on the estimated absolute activity of the one or more metabolic fluxes. In some embodiments, the subject has cancer. In some embodiments, the method further comprises the step of administering the selected therapy to the subject. For example, the method may further comprise administering a selected anti-cancer therapy to the subject based on the activity of the one or more estimated metabolic fluxes.

[0017] In some aspects, the present disclosure provides methods for selecting a therapy for a subject with cancer, including determining the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway, and selecting an inosine monophosphate dehydrogenase (IMPDH) inhibitor for the subject when the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis is increased relative to a threshold.

[0018] In some aspects, the present disclosure provides methods for selecting a therapy for a subject with cancer, including determining the absolute activity of the serine synthesis pathway (e.g., the de novo serine synthesis pathway), and selecting dietary serine restriction for the subject when the absolute activity of the serine synthesis pathway is decreased relative to a threshold.

[0019] In some embodiments, the subject has brain cancer. In some embodiments, the subject has glioblastoma. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1. Data acquisition method. ( Figure 1A ) Metabolites from tissues of orthotopic GBM-bearing mice under different treatment conditions are isotopically labeled at multiple time points to generate a model. ( Figure 1B ) Uniformly labeled 13 C-glucose is infused into patients during brain tumor resection, and plasma and resected tissues are collected for assessment of metabolite labeling. ( Figure 1C ) Plasma enrichment of isotopic glucose is measured by LC-MS. ( Figure 1D ) Relative guanosine monophosphate labeling in human tumors compared to adjacent cortical tissue.

[0021] Figure 2 . Reaction network for quantifying purine pathway fluxes. AMP: adenosine monophosphate; C-THF: formyltetrahydrofolate; CO2: carbon dioxide; IMP: inosine monophosphate; GDP: guanosine diphosphate; GMP: guanosine monophosphate; R5P: ribose-5-phosphate.

[0022] Figure 3. Estimated flux values of the INST-MFA model. Fluxes were estimated under four conditions: GBM without radiotherapy, GBM after radiotherapy, adjacent normal cortical tissue without radiotherapy, and normal cortical tissue after radiotherapy.

[0023] Figures 4A - 4D . MFA revealed higher flux through IMPDH after radiotherapy (RT). (Figure 4A) De novo GMP synthesis in untreated naive mouse models. (Figure 4B) Dynamic map of IMP (inosine monophosphate) de novo synthesis after RT. IMP is a precursor for de novo GMP synthesis after RT. (Figure 4C) Dynamic map of GMP de novo synthesis. (Figure 4D) Proportion of total GMP flux via IMPDH de novo synthesis after RT. RT: radiotherapy.

[0024] Figure 5 An exemplary architecture of the convolutional neural network (CNN model) described herein is shown.

[0025] Figures 6A - 6H Robust [U 13 C]-glucose uptake and utilization in mouse models of brain cancer and patients are shown. (A) Schematic of [U 13 C]-glucose infusion into patients and mouse models of brain cancer. (B) Example of MRI-defined tissue collection. (C) Clinical and molecular characteristics of patients studied with stable isotope tracing. (D) Time course of M+6 arterial glucose enrichment in patients (upper panel) and mice (lower panel) receiving [U 13 C]-glucose infusion. For mice, error bars represent SD of 2 - 10 mice. (E) Schematic of glucose carbon (red circles) redistribution into glycolytic intermediates. Scrambling can occur via recombination with unlabeled intermediates (E4P, S7P, R5P, GAP) in the pentose phosphate cycle. (F) Average enrichment of glycolytic intermediates in GBM (gold) and cortical (blue) tissues isolated from orthotopic GBM38 tumor-bearing mice (n = 7 mice, error bars represent SD) infused with [U 13 C]-glucose. (G). Normalized (based on plasma M+6 glucose of each patient) enrichment of glycolytic intermediates in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients (n = 7 - 8 samples per group, error bars represent SD) infused with [U 13 C]-glucose. (H) H&E staining (left) and MALDI image of orthotopically grown GBM38 PDX, which shows lactate 13C enrichment, with the tissue maximum set at 100%. *p < 0.05. Metabolite abbreviations are as follows: FBP (fructose bisphosphate), GAP (glyceraldehyde phosphate), DHAP (dihydroxyacetone phosphate), PG (phosphoglyceric acid), PEP (phosphoenolpyruvate), Pyr (pyruvate), Lac (lactate), G6P (glucose 6-phosphate), F6P (fructose 6-phosphate), R5P (ribose 5-phosphate), E4P (erythrose 4-phosphate), S7P (sedoheptulose 7-phosphate), 3PG (3-phosphoglyceric acid).

[0026] Figures 7A - 7I Shows reduced TCA cycle and neurotransmitter markers in brain cancer. (A) Schematic of 13 C labeling of TCA cycle intermediates and neurotransmitters from M+3 pyruvate. Red circles indicate entry through pyruvate dehydrogenase, and orange indicates entry through pyruvate carboxylase. Blue circles indicate the labeling patterns that may occur during the second round of the TCA cycle. (B) Mean enrichments of TCA cycle intermediates and aspartate in GBM (gold) and cortical (blue) tissues isolated from orthotopic GBM38 tumor-bearing mice (n = 7 mice, error bars represent SD) infused with [U 13 C] - glucose. (C) Mean enrichments of glutamine and glutamate in GBM (gold) and cortical (blue) tissues isolated from orthotopic GBM38 tumor-bearing mice (n = 7 mice, error bars represent SD) infused with [U 13 C]-glucose. (D) Normalized (based on plasma M+6 glucose per patient) enrichments of TCA cycle intermediates and aspartate in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients (n = 7 - 8 samples per group, and error bars represent SD) infused with [U 13 C]-glucose. (E) Normalized (based on plasma M+6 glucose per patient) enrichments of glutamine and glutamate in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients (n = 7 - 8 samples per group, error bars represent SD) infused with [U 13 C]-glucose. Mean enrichments (F) and normalized mean enrichments (G) of GABA in mouse (F) and human (G) samples. (H) Mean enrichment of malate normalized by MALDI. Color bar tissue maximum is normalized to 100%. (G) % enrichment of malate in representative human cortex (left), non-enhancing tumor (middle), and enhancing tumor (right). Color bar maximum is set to the true enrichment. Abbreviations: aKG (α-ketoglutarate), NME (normalized mean enrichment). *p < 0.05, **p < 0.01.

[0027] Figure 8A -9H shows increased glucose-driven nucleotide synthesis in brain cancer. (A) Schematic of the purine synthesis pathway. Green and yellow circles represent carbons from glycine and folate, respectively. Blue circles represent carbons from ribose 5-phosphate (R5P) (showing different R5P labeling patterns indicates potential pentose phosphate cycle rearrangements). (B) Average enrichment of purines in GBM (gold) and cortex (blue) tissues isolated from orthotopic GBM38 tumor-bearing mice infused with [U 13 C]-glucose (n = 7 mice, error bars represent SD). (C) Normalized (based on plasma M+6 glucose per patient) enrichment of purines in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients infused with [U 13 C]-glucose (n = 7 - 8 samples per group, error bars represent SD). (D) Schematic of the pyrimidine synthesis pathway. Purple represents carbons from aspartate, blue represents carbons from R5P, and green represents carbons from folate. (E) Average enrichment of pyrimidines in GBM (gold) and cortex (blue) tissues isolated from orthotopic GBM38 tumor-bearing mice infused with [U 13 C6] - glucose (n = 7 mice, error bars represent SD). (F) Normalized (based on plasma M+6 glucose per patient) enrichment of pyrimidines in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients infused with [U 13 C]-glucose (n = 7 - 8 samples per group, error bars represent SD). (G) Normalized (based on plasma M+6 glucose per patient) enrichment of NAD and NADH in cortex (blue), non-enhancing tumor (gray), and enhancing tumor (orange) from 8 patients infused with [U 13 C]-glucose (n = 7 - 8 samples per group, error bars represent SD). (H) AMP M+5 signal intensity in mouse GBM and cortex by MALDI. Color bar tissue maximum is normalized to 100%. Abbreviations: methyl THF (N10-formyltetrahydrofolate). AMP (adenosine monophosphate), IMP (inosine monophosphate), GMP (guanosine monophosphate), GDP (guanosine diphosphate), ADP (adenosine diphosphate), 5,10-MeTHF (5,10-methylenetetrahydrofolate), UMP (uridine monophosphate), CMP (cytidine monophosphate), dTDP (deoxythymidine diphosphate), NAD (nicotinamide adenine dinucleotide oxidized form), NADH (nicotinamide adenine dinucleotide reduced form). *p < 0.05, **p < 0.01, ***p < 0.001.

[0028] Figures 9A - 9F Quantification of metabolic fluxes in GBM and cortex is shown. (A) Schematic. [U 13 C]-glucose was infused into GBM38 PDX-bearing mice. Mice were serially euthanized at different time points (0, 30, 120, and 240 min), and GBM and cortex were harvested to measure metabolite enrichment and estimate metabolic fluxes. (B–C) Absolute fluxes of purine (B) and pyrimidine (C) synthesis reactions in cortex (left) and GBM (right). * indicates p < 0.05 compared to cortex. (D–E) Percent abundances of individual malate isotopologues in cortex (D) or GBM (E), error bars represent SD of n = 3–9 data points from n = 1–3 mice at each time point. (F) Percent change of indicated malate isotopologues from 120 to 240 min. Error bars were derived from the uncertainty of 120 and 240 min data points in (D) and (E).

[0029] Figure 10A -10I shows the dynamic metabolic response to radiation in GBM and cortex. (A) Schematic of the dynamic metabolic flux analysis pipeline. (B) Overview of the purine synthesis pathway. (C–I) Dynamic metabolic fluxes in GBM (red) and cortex (gray) after RT. At t = 0, GBM38 PDX-bearing mice were treated with cranial RT (8 Gy). Mice were serially euthanized at different time points after RT (0, 30, 60, 120, and 240 min), and GBM and cortex were harvested to estimate metabolic fluxes (n = 1–3 mice per group, with 1–3 samples / mouse). Solid lines represent the estimated fluxes, and the shaded areas represent 95% confidence intervals. Abbreviations: Me-THF (again, I think this is N 10 -formyltetrahydrofolate), R5P (ribose 5-phosphate), IMP (inosine monophosphate), AMP (adenosine monophosphate).

[0030] Figures 11A - 11H Preference for environmental serine in brain cancer is shown. (A) Mean 13 C enrichment of serine in cortex (n = 7) or orthotopic GBM38 PDX (n = 7). (B). Normalized (based on plasma glucose enrichment) mean enrichment of 13 C in serine in human samples (n = 7–8 per group). (C) 13Percentage of serine in C atoms. (D) Serine isotopologue distribution in tissues from 8 human brain cancer patients. Error bars represent SD of 3 technical replicates per patient. (E) Isotopologue distribution of plasma serine and tissue phosphoglycerate (PG) in PDX. (F) Isotopologue distribution of plasma serine and tissue PG in human tissues (PG normalized according to plasma glucose enrichment). (G) Metabolic flux analysis model for estimating the pathways of serine synthesis in cortex and brain cancer. (H) Dependence on serine uptake relative (to cortex) compared to glucose-driven de novo serine synthesis. Significance was tested by comparing the 95% confidence intervals of the flux models. * indicates p < 0.05 compared to 1.0 (i.e., significantly different from cortex).

[0031] Figures 12A - 12JDietary serine restriction is shown to selectively alter GBM metabolism and slow tumor growth. (A) Representative bioluminescence imaging of orthotopically growing GBM38 PDX in mice on control (top panel) or serine / glycine (Ser / Gly)-restricted diet (bottom panel). (B) Fold change in luminescence of GBM38 PDX-bearing mice fed control diet (black) or Ser / Gly-restricted diet (red) (compared to mean luminescence at day 3). Error bars represent SEM for 9-10 animals per group. (C-G) Mice in panel B were euthanized approximately 4 weeks after implantation, and the brains were cut in half for histopathology (C-E) or metabolomics (F-G) analysis. (C-D) Representative H&E (C) or Ki-67 immunohistochemistry (D) images from mice on control or Ser / Gly-restricted diet. (E) Ki-67 quantification of GBM38 tumors from mice on control diet (black, n = 5) or Ser / Gly-restricted diet (red, n = 4). (F) Heatmap of relative metabolite levels (top 65 PLS-DA) in orthotopic GBM38 tumors from mice fed control (n = 4) or Ser / Gly-restricted diet (n = 5), with each row representing an individual tumor. (G) Relative serine and phosphoserine levels in GBM38 tumors and cortex from mice fed control or Ser / Gly-restricted diet. Error bars represent SD. (H-J) Model of cortical metabolic rewiring in brain cancer. (H) Cortex takes up large amounts of glucose to fuel the TCA cycle and synthesis of the neurotransmitters serine, GABA, and glutamate. (I) Brain cancer upregulates uptake of ambient serine and downregulates oxidation of glucose in the TCA cycle and glucose-derived neurotransmitter synthesis. Tumors also reroute glucose-derived carbon to synthesize nucleotides and NAD / NADH to drive tumor growth. (J) Restricting dietary serine forces gliomas to reroute glucose carbon towards serine synthesis, thereby reducing nucleotide and NAD / NADH levels and slowing tumor growth. *p < 0.05, **p < 0.01.

[0032] Figures 13A - 13D Circulating lactate enrichment and sample histology are shown. (A). Time course of M+3 lactate in plasma of patients infused with [U 13 C]-glucose. (B). From patients infused with [U 13Time course of M+3 lactate in plasma of orthotopic GBM-bearing mice with [[C]]-glucose (n between 2 and 10 per time point). Data are shown as mean ± standard deviation. (C) Representative hematoxylin and eosin staining of tissue resected from our patient cohort. (D) Percentage of tumor content in tissue from each patient was defined by a clinical neuropathologist (SV). Data are shown as mean ± standard deviation, n = 8 patients. *p < 0.05. **P < 0.01. ns, not significant. Abbreviations: NAA, N-acetylaspartate.

[0033] Figures 14A - 14D Altered metabolite abundances in gliomas compared to normal cortex are shown. (A) NAA levels in cortical and tumor tissues (enhanced and non-enhanced) of human glioma patients who underwent surgical resection. Volcano plots of metabolite abundances measured by LC-MS were used to compare fold changes in tumor metabolite levels compared to cortical metabolite levels as follows: (B) cortex versus enhanced tumor in patients, (C) cortex versus non-enhanced tumor in patients, and (D) cortex versus GBM in orthotopic GBM-bearing mice. **p < 0.01. Abbreviations: NAA, N-acetylaspartate; NAAG, N-acetylaspartylglutamate; GMP, guanosine monophosphate.

[0034] Figures 15A - 15B Isotopic enrichments of UDP-glucose in cortex and gliomas are shown. (A) UDP-glucose M+6, mainly derived from M+6 glucose (left), and fractional enrichment of UDP-glucose, as a fraction of all 13 [[C]] isotope species (right). N = 7 mice. (B) Normalized (based on plasma m+6 glucose per patient) M+6 UDP-glucose enrichment in tissues from glioma patients infused with [[U]] 13 [[C]]-glucose. Data are shown as mean ± standard deviation. *P < 0.05. ns, not significant.

[0035] Figure 16A -16G shows spatially defined isotope labeling in mouse brain and GBM. (A) Hematoxylin and eosin staining of brains of orthotopic GBM-bearing mice intraperitoneally injected with a negative carrier (as a negative control for insets B-G) or [[U]] 13 [[C]]-glucose. MALDI-MS was used to determine the 13 [[C]] enrichment of (B) lactate, (C) aspartate, (D) GABA, (E) glutamate, (F) glutamine, and (G) AMP M+5. Tissue maximum was set to 100%. Abbreviations: GABA, γ-aminobutyric acid; AMP, adenosine monophosphate.

[0036] Figures 17A - 17CSpatial - defined isotope labeling in human cortex and gliomas is shown. Specified tissue types resected from brain cancer patients who received [U 13 C]-glucose infusion (Patients 1 - 8) or no infusion (Unlabeled 1, 2) were evaluated for 13 C isotope labeling of (A) malate, (B) glutamate, and (C) glutamine by MALDI - MS.

[0037] Figures 18A - 18C Enrichment of 13 C - labeled metabolites quantified by spatial MALDI - MS is shown. 13 C labeling of (A) malate, (B) glutamate, and (C) glutamine for all data points of spatial MALDI - MS scans of tissues resected from glioma patients (as shown in Figure 16). Patients 1 - 8 were infused with [U 13 C]-glucose, and Patients I and II did not receive infusion. The line within each box represents the median, the box represents the interquartile range, the whiskers represent the minimum and maximum values, and the points outside the whiskers represent outliers.

[0038] Figures 19A - 19B Production of ribose 5 - phosphate from glucose in cortex and brain tumors is shown. (A) Percent enrichment of ribose 5 - phosphate in tissues from orthotopic GBM - bearing mice (n = 7) infused with [U 13 C]-glucose. (B) Enrichment of normalized (based on plasma m + 6 glucose per patient) ribose 5 - phosphate in cortex and tumor tissues from glioma patients infused with [U 13 C]-glucose. Data are shown as mean ± standard deviation. ns, not significant.

[0039] Figures 20A - 20D Production of glucose - derived inosylate and adenylate purine metabolites in human cortex and gliomas is shown. (A) Normalized (based on plasma m + 6 glucose per patient) enrichment of IMP, (B) inosine, (C) AMP, and (D) ADP. Data are shown as mean ± standard deviation. *p < 0.05. **p < 0.01. ***p < 0.001. ****p < 0.0001. ns, not significant. Abbreviations: IMP, inosine monophosphate; AMP, adenosine monophosphate; ADP, adenosine diphosphate.

[0040] Figures 21A - 21CShows the production of glucose-derived guanine purine metabolites in human cortex and glioma. (A) Guanosine, (B) GMP, and (C) Normalized (based on plasma m+6 glucose per patient) enrichments of GDP. Data are shown as mean ± standard deviation. *p<0.05. **p<0.01. ***p<0.001. ****p<0.0001. Abbreviations: GMP, guanosine monophosphate; GDP, guanosine diphosphate.

[0041] Figures 22A - 22B Shows the production of glucose-derived pyrimidine metabolites in human cortex and glioma. (A) UMP and (B) Normalized (based on plasma m+6 glucose per patient) enrichments of dTDP. Data are shown as mean ± standard deviation. *p<0.05. **p<0.01. ***p<0.001. ****p<0.0001. Abbreviations: UMP, uridine monophosphate; dTDP, deoxythymidine diphosphate.

[0042] Figures 23A - 23B Shows the production of glucose-derived NAD in cortex and GBM. (A) Schematic of carbon incorporation into NAD and NADH. (B) 13 13C enrichments of NAD and NADH in cortex and GBM tissues from orthotopic GBM-bearing mice infused with [U 13 13C]-glucose. Data are shown as mean ± standard deviation. N = 7 mice. **p<0.01. Abbreviations: NAM, nicotinamide; ATP, adenosine triphosphate; NAD, nicotinamide adenine dinucleotide; NADH, nicotinamide adenine dinucleotide reduced form.

[0043] Figures 24A - 24C Shows the time-course of [U 13 13C]-glucose carbon incorporation into nucleotide metabolites in cortex and GBM. (A) Time-dependent enrichment profiles of purine metabolites IMP, GDP, guanosine, AMP, and inosine in cortex and GBM in orthotopic brain tumor-bearing mice infused with [U 13 13C]-glucose. (B) Time-dependent enrichments of pyrimidine metabolites UMP and uridine in cortex and GBM in orthotopic brain tumor-bearing mice infused with [U 13 13C]-glucose. (C) Relative abundances of nucleotide species in cortex and GBM tissues from orthotopic tumor-bearing mice. Data are shown as mean ± standard deviation, n = 3-9 samples from 1-3 mice per time point.

[0044] Figures 25A - 25B Shows a pathway-based framework for in vivo modeling of nucleotide synthesis. Biochemical interconversions and model boundaries for metabolic modeling of (A) purine synthesis and (B) pyrimidine synthesis.

[0045] Figures 26A - 2 6F shows reduced TCA cycle activity of glucose origin in GBM compared to cortex. At the indicated time points, isotopologue abundance levels of citrate in cortex (A) and GBM (B) tissues from orthotopic GBM-bearing mice infused with [U 13 C]-glucose. (C) Percent change in the indicated citrate isotopologues from 120 to 240 min. Error bars were derived from the uncertainty of the t = 120 and t = 240 min data points in (A) and (B). Isotopologue abundance levels of succinate in mouse cortex (D) and GBM (E) infused with [U 13 C]-glucose. (F) Percent change in the indicated succinate isotopologues from 120 to 240 min. Error bars were derived from the uncertainty of the t = 120 and t = 240 min data points in (D) and (E). Data are shown as mean ± standard deviation, n = 6 - 9 samples from 2 - 3 mice per time point.

[0046] Figures 27A - 27B Shows the time-dependent changes in purine synthesis activity in cortex and GBM after RT. Cortex and GBM of orthotopic brain tumor-bearing mice treated with a single dose of cranial RT (8 Gy) and then immediately infused with [U 13 C]-glucose, for the (A) isotopic enrichment and (B) relative abundance of purine metabolites IMP, GDP, guanosine, AMP, and inosine. Data are shown as mean ± standard deviation, n = 3 - 9 samples from 1 - 3 mice per time point.

[0047] Figure 28 Shows the metabolic reaction fluxes in GBM and cortex after RT. Flux values were estimated using time-course enrichment profiles from mice infused with [U 13 C]-glucose as described in the Supplementary Methods.

[0048] Figures 29A - 29B Shows different serine origins in human cortex and brain cancer. (A) Statistical analysis of M+1 and M+3 serine enrichments confirmed that M+1 serine is higher and M+3 serine is lower in brain cancer compared to cortex. Data are shown as mean ± standard deviation. *p < 0.05. **p < 0.01. ***p < 0.001. ****p < 0.0001. (B) The ratio of the contribution of de novo serine synthesis to serine salvage in human cortex and brain cancer. Values above 1 indicate that de novo synthesis is the major source of labeled serine, while values below 1 indicate that serine salvage is the major source of labeled serine. Error bars represent 95% confidence intervals.

[0049] Figures 30A - 30CShows the plasma serine levels and tissue metabolites in orthotopic GBM-bearing mice on a serine / glycine-restricted diet. (A) Serine levels in the plasma of orthotopic GBM-bearing mice fed a control diet or a serine / glycine-restricted diet, with n = 5 mice per group. (B) Principal component analysis of cortical and GBM tissues from mice on a control diet (n = 4) or a serine / glycine-restricted diet (n = 5) in panel A. (C) Individual metabolite levels in cortical tissues from the mice in panel A. One mouse in the control diet group in panel A was found to have no detectable tumor and was thus excluded from the analyses in panels B and C.

[0050] Figure 31 Shows the metabolic fluxes generated by a constrained optimization problem and used to simulate time-course MID. The simulated MID was divided into training, validation, and test datasets. The validation dataset (Val.) was used to tune the hyperparameters in the Bayesian optimization method (BO), with the objective function set as the coefficient of determination (CD) between the predicted and actual values. The test dataset was used to evaluate the model (Eval.) based on unseen data. (2) Three machine learning models were implemented in this study, including two convolutional neural networks (CNNs) and one graph neural network (GNN). (3) The machine learning models were experimentally validated. (4) The machine learning models were applied to predict the rate of de novo GMP synthesis in patients. (5) The predicted rate was further validated by flux balance analysis of patient scRNA-seq data. (6) The machine learning models will be used in clinical trials to recommend which patients can benefit from MMF treatment.

[0051] Figure 32A -32G shows a metabolism-based machine learning model. (A) The metabolic model used in MID simulation and the machine learning model. (B) Simulated flux distribution based on stoichiometric mass balance. (C) The simulated data structure. m, i, and t represent metabolite, MID, and time, respectively. m, n, and k represent the metabolite number, MID number, and time point number, respectively. (D) The first CNN framework. (E) The second CNN framework. (F) The graphical structure of purine metabolism. (G) The GNN framework.

[0052] Figures 33A - 33C Shows machine learning predictions. (A) The first CNN predictions for the training, validation, and test datasets. (B) Experimental validation of the model performance of MMF-treated PDX relative to control PDX. (C) Model predictions for patient-enhanced and non-enhanced tumors.

[0053] Definition

[0054] Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the embodiments described herein, some preferred methods, compositions, devices, and materials are described herein. However, before describing the materials and methods of the present invention, it should be understood that the present invention is not limited to the specific molecules, compositions, methods, or protocols described herein, as these can vary according to routine experiments and optimizations. It should also be understood that the terms used in the specification are for the purpose of describing particular versions or embodiments only and are not intended to limit the scope of the embodiments described herein.

[0055] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. However, in case of conflict, the present specification, including definitions, shall prevail. Accordingly, the following definitions apply in the context of the embodiments described herein.

[0056] Unless the context clearly dictates otherwise, as used herein and in the appended claims, the singular forms "a," "an," and "the" include plural referents.

[0057] As used herein, the term "comprising" and its variations in language denote the presence of one or more of the described features, one or more of the elements, one or more of the method steps, etc., but do not preclude the presence of additional one or more features, one or more of the elements, one or more of the method steps, etc. Conversely, the term "consisting of" and its variations in language denote the presence of one or more of the recited features, one or more of the elements, one or more of the method steps, etc., and exclude any unrecited one or more features, one or more of the elements, one or more of the method steps, etc., except for impurities that are ordinarily associated therewith. The phrase "consisting essentially of" denotes one or more of the recited features, one or more of the elements, one or more of the method steps, etc., and any additional one or more features, one or more of the elements, one or more of the method steps, etc. that do not materially affect the basic properties of the composition, system, or method. Many embodiments herein are described using the open "comprising" language. Such embodiments encompass multiple closed "consisting of" and / or "consisting essentially of" embodiments that can also be alternatively claimed or described using such language.

[0058] The term "absolute metabolic flux" as used herein refers to the total molecular flux through a given metabolic pathway.

[0059] The term "isotopologue" as used herein refers to molecules that have the same chemical formula and atomic bonding arrangement but differ only in their isotopic composition. Isotopologues are also referred to as "mass isotopomers." Due to tracers (e.g. 13the metabolism of C or other suitable tracers), and isotopologues are generated by the methods described herein. The metabolism of the tracer results in the generation of metabolites labeled with the tracer (e.g., labeled with 13 C). For example, a metabolite having n carbon atoms can have 0 to n of its carbon atoms labeled with the tracer (e.g., labeled with 13 C), resulting in isotopologues with a mass (M) ranging from M+0 (all unlabeled carbons) to M+n (all labeled carbons).

[0060] The term "subject" is used herein in the broadest sense and refers to any living organism in which metabolic flux can be evaluated. In some embodiments, the subject is an animal. In some embodiments, the subject is a vertebrate. In some embodiments, the subject is a bird. In some embodiments, the subject is a mammal. Suitable mammals include, but are not limited to, mammals of the order Rodentia, such as mice and hamsters, and mammals of the order Lagomorpha, such as rabbits, mammals of the order Carnivora, including Felines (cats) and Canines (dogs), mammals of the order Artiodactyla, including Bovines (cows) and Swines (pigs), or mammals of the order Perissodactyla, including Equines (horses). In some aspects, the mammal belongs to the order Primates, the family Cebidae or Simiidae (monkeys), or the order Anthropoidea (humans and apes). In some aspects, the mammal is a human. In some embodiments, the subject is a plant. DETAILED DESCRIPTION

[0061] In some aspects, provided herein are methods for estimating the absolute metabolic flux of a pathway of interest. In some embodiments, the method for estimating the absolute metabolic flux of a pathway of interest includes administering a tracer to a subject, collecting a sample from the subject, and generating an estimate of the absolute metabolic flux of the pathway of interest. In some embodiments, the sample is a tissue sample.

[0062] In some embodiments, the estimated results of the absolute metabolic flux of the pathway of interest are generated based on the levels of one or more metabolites and / or their isotopologues in a sample at a single time point after administration of a tracer to a subject. In some embodiments, the levels of one or more metabolites and / or isotopologues are measured in the sample. For example, any suitable technique can be used to measure the levels of one or more metabolites and / or their isotopologues in the sample, including mass spectrometry-based methods (e.g., liquid chromatography-mass spectrometry (LC-MS)), nuclear magnetic resonance (NMR) spectroscopy, or other suitable methods. In some embodiments, the level of a given metabolite or its isotopologue is measured in the sample at a time point after administration of the tracer. In some embodiments, the level of a given metabolite or its isotopologue is measured in the sample at a time point after administration of radiotherapy.

[0063] In some embodiments, the pathway of interest is the purine synthesis pathway. In some embodiments, the pathway of interest is the purine synthesis pathway, and one or more metabolites and / or their isotopologues include one or more of the following: ribose-5-phosphate (R5P), glycine (GLY), carbon dioxide (CO2), 5-methyltetrahydrofolate (C-THF), inosine monophosphate (IMP), inosine, hypoxanthine, guanine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine, adenosine monophosphate (AMP), and adenosine. In some embodiments, one or more metabolites and / or their isotopologues include at least 2, at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, at least 10, at least 11, at least 12, or each of ribose-5-phosphate (R5P), glycine (GLY), carbon dioxide (CO2), 5-methyltetrahydrofolate (C-THF), inosine monophosphate (IMP), inosine, hypoxanthine, guanine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine, adenosine monophosphate (AMP), and adenosine.

[0064] In some embodiments, the purine synthesis pathway includes multiple reactions. Exemplary reactions in the purine synthesis pathway are shown in Figure 25A . In some embodiments, generating the estimated results of the absolute metabolic flux of the purine synthesis pathway includes determining the total flux through the multiple reactions involved in the purine synthesis pathway. For example, in some embodiments, generating the estimated results of the absolute metabolic flux of the purine synthesis pathway includes determining the flux through Figure 25AThe total flux of each reaction shown. In some embodiments, the method further includes determining the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway. "Contribution ratio" refers to the portion of the estimated result of the absolute metabolic flux that can be attributed to (e.g., contributed by) de novo GMP synthesis and / or de novo IMP synthesis.

[0065] In some embodiments, the pathway of interest is the pyrimidine synthesis pathway. In some embodiments, the pathway of interest is the pyrimidine synthesis pathway, and one or more metabolites and / or their isotopologues include one or more of ribose-5-phosphate (R5P), aspartate (ASP), carbon dioxide (CO2), uridine, and uridine monophosphate (UMP). In some embodiments, one or more metabolites and / or their isotopologues include at least 2, at least 3, at least 4, or each of ribose-5-phosphate (R5P), aspartate (ASP), carbon dioxide (CO2), uridine, and uridine monophosphate (UMP). In some embodiments, the pyrimidine synthesis pathway includes multiple reactions. Exemplary reactions in the pyrimidine synthesis pathway are shown in Figure 25B In some embodiments, generating an estimated result of the absolute metabolic flux of the pyrimidine synthesis pathway includes determining the total flux through the multiple reactions involved in the pyrimidine synthesis pathway. For example, in some embodiments, generating an estimated result of the absolute metabolic flux of the pyrimidine synthesis pathway includes determining the total flux through Figure 25B each reaction shown.

[0066] In some embodiments, the pathway of interest is the serine synthesis pathway (e.g., de novo serine synthesis pathway). In some embodiments, the pathway of interest is the serine synthesis pathway, and the one or more metabolites and / or their isotopologues include one or more of 3-phosphoglycerate (3PG), glycine (gly), and 5,10-methylene THF (Me-THF).

[0067] In some embodiments, the levels of one or more metabolites and / or their isotopologues are increased upon measurement. Accordingly, the estimation results of the absolute metabolic fluxes of the pathways of interest are also described herein as being generated based on the enrichments of one or more isotopologues of at least one metabolite of interest measured at a given time point (e.g., after administration of a tracer and / or after administration of radiotherapy to a subject). Thus, measuring the levels of one or more metabolites and / or their isotopologues is also referred to herein as measuring the “enrichment” of one or more isotopologues of at least one metabolite of interest at a given time point after administration of radiotherapy to a subject. For example, measuring the “enrichment” or “enriched” levels can refer to an increase in the level of a given metabolite or its isotopologue at a given time point (e.g., upon measurement) compared to other time points or compared to a baseline level. In some embodiments, the baseline level is measured. For example, in some embodiments, the baseline level is measured before radiotherapy and / or before administration of a tracer to a subject. In some embodiments, the baseline level is obtained in other ways, such as estimating the amount of a given metabolite in a particular tissue based on knowledge in the literature or based on measurements inferred from other sources.

[0068] In some embodiments, the estimation results of the absolute metabolic fluxes of the metabolites of interest are generated using an artificial intelligence / machine learning (AI / ML) model. An AI / ML model refers to a mathematical algorithm that is trained using data and / or human input to make predictions. The AI / ML model can use any one or more algorithms, including linear regression, logistic regression, linear discriminant analysis, decision trees, naive Bayes, K-nearest neighbors, learning vector quantization, support vector machines, bagging and random forests, and / or neural networks (e.g., deep neural networks). Exemplary algorithms and equations for estimating absolute metabolic fluxes are shown in the accompanying examples.

[0069] In some aspects, provided herein is a machine learning method for estimating the absolute activity of one or more metabolic fluxes. In some embodiments, the machine learning method is used to estimate the absolute activity of a single enzyme (e.g., estimating the absolute activity of a single enzyme in a given metabolic pathway). In some embodiments, the machine learning method is used to estimate the absolute activity of a metabolic pathway (e.g., a pathway affected by multiple enzymes).

[0070] In some embodiments, the machine learning method for estimating the absolute activity of one or more metabolic fluxes includes obtaining a plurality of measurements from a sample collected from a subject and applying an artificial intelligence / machine learning model to these measurements to generate an estimation result of the absolute activity of one or more metabolic fluxes.

[0071] In some embodiments, each measurement is the level of a metabolite and / or its isotopologue in a metabolic pathway of interest at a single time point. The level of one or more metabolites and / or their isotopologues can be measured in a sample using any suitable technique, including mass spectrometry-based methods (e.g., liquid chromatography-mass spectrometry (LC-MS), nuclear magnetic resonance (NMR) spectroscopy, or other suitable methods). In some embodiments, multiple measurements are obtained at a single time point after administration of a tracer to a subject. In some embodiments, multiple measurements are obtained at a single time point after administration of radiotherapy to a subject.

[0072] In some embodiments, the level of one or more metabolites and / or their isotopologues is increased at the time of measurement. Thus, the method can also be described herein as involving obtaining multiple measurements from a sample, where each measurement is a measurement of the "enrichment" of one or more metabolites or their isotopologues. For example, measuring the "enrichment" or "enriched" level can refer to an increase in the level of a given metabolite or its isotopologue at a given time point (e.g., at the time of measurement) compared to other time points or compared to a baseline level. In some embodiments, the baseline level is measured. For example, in some embodiments, the baseline level is measured before radiation and / or before administration of a tracer to a subject. In some embodiments, the baseline level is obtained otherwise, such as by estimating the amount of a given metabolite in a particular tissue based on knowledge in the literature or based on measurements inferred from other sources.

[0073] In some embodiments, the method further comprises applying an artificial intelligence / machine learning (AI / ML) model to the measurements to generate an estimate of the absolute activity of one or more metabolic fluxes. The AI / ML model can use any one or more algorithms, including linear regression, logistic regression, linear discriminant analysis, decision trees, naive Bayes, K-nearest neighbors, learning vector quantization, support vector machines, bagging, and random forests and / or neural networks (e.g., deep neural networks). In some embodiments, the AI / ML model uses a neural network.

[0074] For any embodiment of the present disclosure, a subject may have or be at risk of having a disease or disorder for which an assessment of metabolic flux can be useful, such as for guiding the selection of a therapy for the disease or disorder. In some embodiments, the subject has or is suspected of having cancer. In some embodiments, the subject has cancer and the tissue sample comprises a tumor tissue sample. In some embodiments, the cancer is brain cancer. In some embodiments, the brain cancer is glioblastoma. In some embodiments, the subject is a candidate for radiotherapy or has received radiotherapy. In some embodiments, an estimate of the absolute metabolic flux of a pathway of interest is generated based on the levels of one or more metabolites and / or their isotopologues at a single time point after administration of radiotherapy to the subject.

[0075] In some embodiments, an estimate of the absolute metabolic flux of a metabolic pathway of interest can be used for personalized medicine, including guiding the selection of a therapy for a subject having cancer (such as having brain cancer, including glioblastoma). For example, based on an estimate of the absolute metabolic flux generated for a subject using the methods described herein, the subject can be identified as likely to be sensitive or resistant to a given therapy targeting a given metabolic pathway. Thus, in some aspects, the present disclosure provides a method of selecting a therapy for a subject in need thereof (including a subject having cancer). The method includes generating an estimate of the absolute metabolic flux using the methods described herein and selecting a suitable therapy (such as an anti-cancer therapy) for the subject based on the estimate of the absolute metabolic flux. The term "selecting" is used in the broadest sense and includes identifying that a patient is sensitive to a therapy, recommending a therapy to the subject, and / or administering a therapy to the subject. In some embodiments, the therapy is an IMPDH inhibitor. In some embodiments, an increased contribution of de novo GMP synthesis and / or increased de novo IMP synthesis in the subject (such as in a sample obtained from the subject and evaluated by the methods described herein) indicates that the subject is sensitive to treatment with an IMPDH inhibitor. In some embodiments, the therapy is dietary restriction of an amino acid. In some embodiments, the therapy is dietary restriction of amino acids such as serine and glycine. In some embodiments, the therapy is serine dietary restriction. Serine dietary restriction includes dietary restriction of serine and any additional amino acids (such as glycine). In some embodiments, the therapy is serine and glycine dietary restriction. In some embodiments, reduced serine synthesis in the subject indicates that the subject is sensitive to dietary restriction of an amino acid (such as serine dietary restriction or serine and glycine dietary restriction).

[0076] In some embodiments, the estimated results of the absolute activity of one or more metabolic fluxes are used in personalized medicine, including guiding therapy selection for a subject with cancer. For example, based on the estimated results of the absolute activity of a metabolic flux (e.g., the activity of a given enzyme in a metabolic pathway) determined using the methods described herein, a subject can be identified as likely to be sensitive or resistant to a given treatment targeting a given metabolic pathway. Thus, in some aspects, the present disclosure provides methods for selecting an appropriate therapy for a subject in need thereof, including an appropriate anti-cancer therapy for the subject. The method includes estimating the absolute activity of one or more metabolic fluxes in a subject using the methods described herein and selecting an appropriate therapy (e.g., an anti-cancer therapy) based on the estimated absolute activity.

[0077] In some aspects, the methods provided herein can be used to determine which subjects will be sensitive to treatment with IMPDH inhibitors or agents targeting de novo GMP synthesis. In some embodiments, subjects having increased de novo GMP synthesis (or increased de novo IMP synthesis, which is a precursor to de novo GMP synthesis), such as subjects with brain cancer, including subjects with glioblastoma, are identified as being sensitive to treatment with IMPDH inhibitors or agents targeting the de novo pathway such as 5-fluorouracil. In some embodiments, methods are provided for selecting a therapy for a subject having cancer, the method comprising determining the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway, and selecting an inosine monophosphate dehydrogenase (IMPDH) inhibitor for the subject when the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis is increased relative to a threshold. The threshold can be the value of de novo GMP and / or de novo IMP synthesis in a control subject or from a control tissue (e.g., tissue not affected by cancer). In some embodiments, the IMPDH inhibitor is a reversible inhibitor, a synthetic non-nucleoside inhibitor, a non-nucleoside natural product inhibitor, a parasite-selective IMPDH inhibitor, a reversible nucleoside inhibitor, or a mechanism-based IMPDH inactivator. In some embodiments, the IMPDH inhibitor is mycophenolate mofetil (MMF), mycophenolic acid (MPA) or a derivative thereof, tiazofurin, ribavirin, VX-994, VX-497, FF-10501, thiazole-4-carboxamide adenine dinucleotide (TAD), nicotinamide adenine dinucleotide (MAD), benzamide riboside, mizorbine, EICAR, selenazofurin, thiophenfurin, myricetin, gnidilatimonoein, VS-148, BMS-566419, BMS-337197, or AS2643361. In some embodiments, the method further comprises administering the IMPDH inhibitor to the subject.

[0078] In some aspects, the methods provided herein can be used to determine which subjects will be sensitive to treatment with amino acid dietary restriction (e.g., serine dietary restriction or serine and glycine dietary restriction). In some embodiments, subjects with reduced de novo serine synthesis (e.g., subjects with brain cancer, including subjects with glioblastoma) are identified as being sensitive to serine dietary restriction treatment. In some embodiments, methods for selecting a therapy for a subject with cancer are provided herein, the method comprising determining the absolute activity of a serine synthesis pathway (e.g., de novo serine synthesis), and when the absolute activity of the serine synthesis pathway is reduced relative to a threshold, selecting serine dietary restriction for the subject. The threshold can be the value of serine synthesis in a control subject or from a control tissue (e.g., tissue not affected by cancer).

[0079] For any of the methods described herein, the term "tracer" is used in the broadest sense and refers to any moiety including a label that can be incorporated into a metabolite during metabolism. In some embodiments, the tracer comprises a moiety labeled with 13 C, 15 N, 18 O or 2 D. The moiety can be any suitable moiety, including but not limited to glucose, methionine, serine, glutamine, lactate, acetate, hypoxanthine, uridine, and water. In some embodiments, the moiety is glucose. In some embodiments, the tracer comprises 13 C-glucose.

[0080] For any of the methods described herein, the subject can be any subject, including human and non-human subjects. In some embodiments, the subject is a vertebrate. In some embodiments, the subject is a mammal. In some embodiments, the subject is a human.

[0081] In some embodiments, a sample is obtained from the subject and the levels of one or more metabolites and / or isotopologues from the sample are analyzed. In some embodiments, the sample comprises tumor tissue (e.g., a biopsy, tumor tissue removed during surgery, etc.). In some embodiments, the tracer is administered to the subject before or during the surgery to remove the sample from the subject's body. For example, the tracer can be administered one minute or several minutes or one hour or several hours before surgery. The tracer can be administered via any suitable means. Suitable routes of administration include but are not limited to oral, sublingual, buccal, rectal, vaginal, ocular, nasal, transdermal, parenteral, inhalation, etc. In some embodiments, the tracer is administered orally. In some embodiments, the tracer is administered parenterally (e.g., by injection, including intravenous, intramuscular, intrathecal, subcutaneous, parenchymal, intraventricular, etc.).

[0082] For any of the methods described herein, the levels of one or more metabolites and / or their isotopologues can be measured at any suitable time point after administration of the tracer. For example, in some embodiments, in a sample from about 1 minute to about 5 hours after administration of the tracer. For example, in some embodiments, at about 1 minute, about 5 minutes, about 10 minutes, about 15 minutes, about 20 minutes, about 25 minutes, about 30 minutes, about 35 minutes, about 40 minutes, about 45 minutes, about 50 minutes, about 55 minutes, about 60 minutes, about 65 minutes, about 70 minutes, about 75 minutes, about 80 minutes, about 85 minutes, about 90 minutes, about 95 minutes, about 100 minutes, about 105 minutes, about 110 minutes, about 120 minutes, about 2.5 hours, about 3 hours, about 3.5 hours, about 4 hours, about 4.5 hours, or about 5 hours after administration of the tracer to measure the levels.

[0083] For any of the methods described herein, the levels of one or more metabolites and / or their isotopologues can be measured at any suitable time point after administration of radiotherapy to a subject. For example, in some embodiments, in a sample from about 1 minute to about 5 hours after administration of radiotherapy to the subject. For example, in some embodiments, at about 1 minute, about 5 minutes, about 10 minutes, about 15 minutes, about 20 minutes, about 25 minutes, about 30 minutes, about 35 minutes, about 40 minutes, about 45 minutes, about 50 minutes, about 55 minutes, about 60 minutes, about 65 minutes, about 70 minutes, about 75 minutes, about 80 minutes, about 85 minutes, about 90 minutes, about 95 minutes, about 100 minutes, about 105 minutes, about 110 minutes, about 120 minutes, about 2.5 hours, about 3 hours, about 3.5 hours, about 4 hours, about 4.5 hours, or about 5 hours after administration of radiotherapy to the subject to measure the levels.

[0084] Examples

[0085] Example 1

[0086] In vivo model system

[0087] To generate data for flux modeling, patient-derived xenografts (PDX) from human glioblastoma were implanted into the brains of immunodeficient mice. Prior to imaging and physical separation from the brain tissue, the PDX were transduced with luciferase and EGFP, respectively. Once the brain tumors were established, the mice were cannulated for infusion, treatment, and blood sampling. A catheter was surgically placed into the jugular vein of anesthetized recipient mice, and a second infusion line was placed into the carotid artery. In experiments where the mice received oral administration of MMF or vehicle, a third catheter was inserted into the stomach. After surgical recovery, the mice were treated with cranial radiotherapy and / or MMF (via the gastric line) and then infused via the jugular vein with uniformly labeled 13C-glucose. Infusion was performed while the mice were awake and active. Aliquots of blood were collected from the jugular infusion catheter into EDTA-coated tubes every 5 - 60 minutes for plasma preparation. At the end of the infusion, the mice were sacrificed and tissues were collected. Brain tumors were separated from healthy brain tissue by fluorescence-guided microdissection. All samples were immediately snap-frozen in liquid nitrogen and stored at -80 °C. Small molecules were extracted from solid tissues and plasma, and the samples were analyzed by liquid chromatography - mass spectrometry (LC-MS) to identify metabolites and their labeling patterns ( Figure 1A ).

[0088] Human isotope labeling

[0089] During clinically indicated resection, uniformly labeled 13 C-glucose ( Figure 1B ) was infused into patients suspected of having GBM via an IV catheter. At fixed time points before and during the infusion, blood was collected from the arterial catheter ( Figure 1C ). When the neurosurgeon resected the tumor and adjacent normal brain tissue, the resected tissue was immediately snap-frozen in liquid nitrogen in the operating room (<2 min after tissue removal). Metabolites were then extracted and metabolite labeling was evaluated by LC-MS as in the mouse model above ( Figure 1D ).

[0090] Quantification of absolute metabolic fluxes in the purine pathway

[0091] Model setup and optimization

[0092] To quantify the fluxes in the purine pathway, an isotopic nonstationary metabolic flux analysis (INST-MFA) methodology was developed. This method addresses several challenges in in vivo flux quantification: (1) Metabolite uptake and secretion fluxes (i.e., exchange fluxes) cannot be experimentally measured. (2) In vivo experiments are resource-intensive and can only be performed for a few hours, which is not sufficient to reach isotopic steady state. (3) Inter-organ metabolism leads to secondary enrichment of circulating metabolites. To overcome these challenges, piecewise linear functions were fitted to the enrichments obtained experimentally for metabolites taken up from outside the reaction network (referred to as "external metabolites", Equation 1).

[0093] The isotope mass balance is applied to metabolites within the reaction network (designated as "internal metabolites") to generate a system of ordinary differential equations (ODEs) (Equation 2). These ODEs are solved together with linear mass balance constraints and physiologically defined parameter bounds (Equation 3). The parameter vector includes network fluxes, pool sizes of internal metabolites, and time-course enrichments of external metabolites. To select the optimal parameters, the time-course enrichments of all metabolites are simulated (Equations 1 and 2), and an objective function is defined to evaluate the fit of the model to the experimental data. The objective function is defined as the sum of the squared errors between the simulated and experimental values, scaled by the standard deviation of the experimental values (Equation 4).

[0094] These experimental values include the enrichments of internal and external metabolites, as well as known pool sizes. The pool sizes of metabolites in mouse brain were obtained from the literature (Table 1), and the corresponding pool sizes for GBM tissue were estimated based on the relative peak areas of mass spectrometry experiments. The Artelys Knitro solver was used to implement an iterative local optimization method based on the interior point / conjugate gradient algorithm (Byrd, R.H. et al. (2006) KNITRO: An integrated package for nonlinear optimization. Nonconvex Optim 83, 35; Byrd, R.H. et al. (1999) An interior point algorithm for large-scale nonlinear programming. Siam J Optimiz 9, 877-900.). Local optimization was performed from 100 randomly assigned initial points, and a set of parameters with the lowest objective function within the statistically acceptable range defined by the chi-square distribution was selected. As described previously, a parameter sensitivity method was implemented to estimate the 95% confidence intervals of the optimized parameters (Antoniewicz, M.R. et al. (2006) Determination of confidence intervals of metabolic fluxes estimated from stable isotope measurements. Metabolic Engineering 8, 324-337).

[0095] Table 1: Concentrations of purine metabolites in mouse brain

[0096] Metabolite Concentration ± SD (pmol / mg tissue) Source Inosine 126.7±18.3 [4] GMP 157±40 [5] GDP 182.1±8.2 [6] Guanosine 245.8±31.6 [4] AMP 172.1±6 [6]

[0097] INST-MFA model equations

[0098] Equation 1:

[0099]

[0100] Equation 2:

[0101]

[0102] Equation 3:

[0103] S.v = 0

[0104] Equation 4:

[0105]

[0106] Table 2 provides a description of the variables in Equations 1 - 4.

[0107] Table 2: Description of variables in INST - MFA Equations 1 - 4.

[0108]

[0109] Reaction network and results

[0110] The metabolic network consists of 15 reactions and 13 metabolites in the purine pathway ( Figure 2 ). Six metabolites are designated as internal metabolites: inosine monophosphate (IMP), inosine, guanosine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), and adenosine monophosphate (AMP). Seven metabolites are designated as external metabolites: ribose - 5 - phosphate (R5P), glycine, formyl - THF, carbon dioxide, hypoxanthine, guanine, and adenosine. Among these, only R5P, glycine, and formyl - THF had their isotope enrichments measured in the experiment. Figure 3 depicts the quantified fluxes.

[0111] Quantification of post - irradiation dynamic metabolic fluxes

[0112] Model setup and optimization

[0113] A dynamic MFA model was established to quantify the flux profiles in the purine pathway after irradiation (Equations 1, 5, 6). The time-dependent enrichments of external metabolites were described by piecewise linear functions, as in the case of INST-MFA (Equation 1). In addition to using time-dependent enrichments and initial metabolite pool sizes in the model, the time-dependent changes in internal metabolite concentrations were also included in the model objective (Equation 7). The in vivo INST-MFA method was modified by describing fluxes as time-dependent B-splines (Martinez, V.S. et al. (2015) Metab Eng Commun 2, 46 - 57; Quek, L.E. et al. (2020) iScience 23, 100855). Through trial and error, third-order B-splines were determined to be suitable for simulating fluxes in this system. An iterative method was used to optimize the number and positions of the internal nodes of the B-splines. Once the positions of one or more nodes were selected, local optimization was performed from 100 initial guesses. The flux solutions from the INST-MFA model were also included in a set of initial guesses under control and RT conditions. The set of parameters with the lowest objective value was selected, and a likelihood-based method was applied to estimate the 95% confidence intervals (Kreutz, C. et al. (2012) Likelihood based observability analysis and confidence intervals for predictions of dynamic models. BMC Syst Biol 6, 120. 10.1186 / 1752 - 0509 - 6 - 120).

[0114] Model equations for dynamic MFA

[0115] Equation 5:

[0116]

[0117] Equation 6:

[0118]

[0119] Equation 7:

[0120]

[0121] Table 3 provides descriptions of the variables in Equations 5 - 7.

[0122] Table 3: Descriptions of the variables in the dynamic MFA Equations 5 - 7.

[0123]

[0124] Reaction network and results

[0125] The reaction network is the same as the network used in INST-MFA ( Figure 2 ). The best-fit time-course profiles of purine pathway fluxes are depicted in FIGS. 4A-4D and are further described in Example 2.

[0126] Machine learning to estimate relative GMP synthesis in human subjects

[0127] A machine learning-based method is described herein for estimating the fraction of de novo synthesized GMP in GBM patients. This information is used to identify those patients in whom their tumors have a high IMPDH contribution to GMP synthesis and who are expected to benefit more from MMF treatment. A major challenge in estimating fluxes in a human subpopulation is that we are limited to enrichment data from single measurements under isotopically non-steady states. To overcome this challenge, an ODE-based model is used to simulate metabolite enrichments for different flux vectors and then this data is used to fit a convolutional neural network (CNN) model ( Figure 5 ). The model input can be the enrichment of purine metabolites obtained experimentally and the model output can be the fraction of de novo GMP synthesis. The CNN architecture was established to capture the relationships between the first 6 isotopologues of the following four metabolites in the purine pathway: IMP, R5P, GDP, and guanosine. These metabolites were selected based on the quality of the metabolomics data. A 1×4 filter was used for data convolution. The number of filters was optimized as a hyperparameter. An exemplary architecture of the CNN model is shown in Figure 5 .

[0128] Example 2

[0129] Glioblastoma multiforme (GBM) is the most common invasive brain cancer in adults and has a five-year survival rate of less than 10%. Radiation is a common treatment modality for GBM patients, but resistance to radiation is common. Radiation-resistant GBM has high levels of the purine nucleoside guanosine triphosphate (GTP). GTP can promote the survival of glioblastoma tissue after radiation by enhancing DNA repair (e.g., can inhibit the ability of radiation to kill glioblastoma cells). The FDA-approved drug mycophenolate mofetil (MMF), an inhibitor of inosine monophosphate dehydrogenase (IMPDH), inhibits GTP synthesis and improves radiation outcomes in mouse models (Zhou W. et al., Nat Commun. (2020); 11(1):3811).

[0130] IMPDH enzymes promote de novo synthesis of GMP (guanosine monophosphate) and are a promising target for tumors with high IMPDH flux. However, there is a lack of methods for quantifying tumor IMPDH flux. Improved methods for quantifying tumor IMPDH flux would identify patients who would benefit from cancer treatment with MMF or other IMPDH inhibitors. For example, patients identified as having high tumor IMPDH flux may be sensitive to treatment with IMPDH inhibitors after radiotherapy, thus enhancing the efficacy of radiotherapy.

[0131] This paper describes the development and use of methods for in vivo metabolic flux analysis. Specifically, 13C metabolic flux analysis (MFA) was used in a GBM xenograft model to quantify the fluxes in the purine pathway before and after radiotherapy. In addition, 13C-glucose tracers were performed in glioblastoma patients to evaluate IMPDH activity in patient tumors. 13 13C metabolic flux analysis (MFA) was used in a GBM xenograft model to quantify the fluxes in the purine pathway before and after radiotherapy. In addition, 13C-glucose tracers were performed in glioblastoma patients to evaluate IMPDH activity in patient tumors. 13 13C-glucose tracers were performed in glioblastoma patients to evaluate IMPDH activity in patient tumors.

[0132] Materials and Methods: The GBM mouse model was infused with 13C glucose as a tracer at different time points. GBM and normal brain tissues were analyzed by mass spectrometry to obtain the 13C-enrichment time-course profiles of intracellular metabolites. A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time. 13 The GBM mouse model was infused with 13C glucose as a tracer at different time points. GBM and normal brain tissues were analyzed by mass spectrometry to obtain the 13C-enrichment time-course profiles of intracellular metabolites. A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time. 13 A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time.

[0133] For glioblastoma patients, 13C-glucose was infused (intravenously) during tumor resection surgery. The resected tumor tissues were analyzed by mass spectrometry to obtain the 13C-enrichment time-course profiles of intracellular metabolites. A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time. 13 For glioblastoma patients, 13C-glucose was infused (intravenously) during tumor resection surgery. The resected tumor tissues were analyzed by mass spectrometry to obtain the 13C-enrichment time-course profiles of intracellular metabolites. A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time. 13 A system of ordinary differential equations was fitted based on least-squares optimization to estimate the purine pathway fluxes with and without radiotherapy. The changes in metabolite levels after radiotherapy were used to estimate the dynamic fluxes over time.

[0134] Results and Discussion: Quantification of purine fluxes in the mouse model revealed that glioblastoma had higher fluxes through IMPDH compared to normal cortex, making it a tumor-specific target (Figure 4A). Dynamic MFA of the purine pathway revealed that the fluxes through IMP de novo synthesis and GMP de novo synthesis increased after radiotherapy (Figures 4B, 4C). In addition, after radiotherapy, the ratio of the GMP de novo synthesis (i.e., GMP de novo synthesis promoted by IMPDH) flux to the total GMP synthesis flux increased (Figure 4D). Collectively, these data suggest that targeting IMPDH with IMPDH inhibitors such as MMF would be effective after radiotherapy, thus enhancing the efficacy of radiotherapy in glioblastoma.

[0135] Data from patients revealed enrichment patterns similar to those in the mouse model.

[0136] In summary, the present disclosure describes a first-principles method for estimating metabolic fluxes. Specifically, this example demonstrates a method for estimating absolute fluxes in xenograft models. The models described herein reveal that IMPDH can be a GBM-specific target after irradiation. Similar methods can be used to characterize other pathways in different tumor types. It can also be used to characterize patient-derived xenografts to guide precision metabolic therapies.

[0137] Example 3

[0138] The brain consumes large amounts of glucose to power neurophysiological aspects. Brain cancers, such as glioblastoma (GBM), lose some aspects of normal biology and gain the ability to proliferate and invade healthy tissue. Little is known about how brain cancers rewire glucose to power these processes. In this article, 13 13C-labeled glucose was infused into patients and mice with brain cancer to determine the metabolic fate of the carbon from the glucose source in tumors and the cortex. By combining these measurements with quantitative metabolic flux analysis, it was demonstrated herein that the human cortex delivers carbon from glucose to physiological processes including TCA cycle oxidation and neurotransmitter synthesis. In contrast, brain cancers downregulate these physiological processes, acquire alternative carbon sources from the environment, and instead use carbon from the glucose source to produce molecules required for proliferation and invasion. Targeting this metabolic rewiring in mice by dietary modulation selectively alters GBM metabolism and slows tumor growth.

[0139] Gliomas are the most common form of malignant brain tumor, which arise when normal glial cells in the central nervous system transform into invasive cells and invade the brain. Glioblastoma (GBM) is the most common invasive type of brain cancer, characterized by deep invasiveness and treatment resistance. Traditional GBM treatment consists of surgical resection, followed by radiotherapy (RT) and temozolomide (TMZ) chemotherapy. Despite these treatments, GBM always recurs, and most patients die within 1-2 years after diagnosis. The poor prognosis of patients with GBM and other forms of glioma is mainly due to treatment resistance, as extensive genomic heterogeneity among and within tumors limits treatment efficacy. Further understanding of common targetable phenotypes in gliomas can advance efforts to develop new therapies and improve the effectiveness of current standard treatments. Relative to neighboring healthy cells, cancer cells exhibit significant differences in metabolic activity and rewire metabolic fluxes to favor proliferation and treatment resistance. In addition, in gliomas, altered metabolism mediates multiple important pre-tumorigenic processes, including treatment resistance. Therefore, targeting tumor metabolism in patients for therapeutic benefit is an attractive clinical strategy.

[0140] Defining metabolic pathway activity in human cancers is challenging. Positron emission tomography using glucose analogs shows high glucose uptake in GBM and normal cortex, but does not provide information on how these tissues differentially utilize the carbon of glucose sources. Quantifying metabolite abundances (such as by mass spectrometry-based metabolomics or magnetic resonance spectroscopy) can reveal differences in metabolite levels between tumors and brain tissues. However, these steady-state measurements provide minimal information on metabolic pathway activity because the level of a metabolite is a function of its production rate and consumption rate. For example, a high level of a given metabolite can reflect either its increased synthesis (elevated activity) or its decreased consumption (reduced activity). Because these very different biological states may respond differently to therapeutic inhibition, understanding the metabolic pathways active in cancer will help to appropriately guide metabolism-directed therapies.

[0141] Isotope tracing was used herein to directly interrogate metabolic pathway activity in cancer. In this technique, metabolic substrates containing heavy (but non-radioactive) isotopes such as 13 C and 2 H are administered to living systems. By tracing the downstream fates of these isotopes by mass spectrometry or nuclear magnetic resonance-based methods, information can be obtained on which metabolic pathways are active in the system. How active are other metabolic pathways in human brain cancers, and how does brain cancer metabolism differ from cortical metabolism, are questions that have not been answered. To answer these questions, 13 C-labeled glucose was infused into orthotopic GBM-bearing mice and patients with high-grade gliomas, and the fates of glucose carbon into many downstream metabolic pathways in cancerous and cortical brain tissues were evaluated. These mass spectrometry-based measurements were combined with a newly developed in vivo metabolic flux model to quantify the absolute rates of many metabolic reactions. The results herein show that invasive brain cancers divert glucose carbon utilization away from physiological processes such as TCA cycle oxidation and neurotransmitter synthesis, in part by salvaging nutrients such as serine from the environment. Instead, they preferentially utilize glucose carbon to synthesize the molecules they need to grow: purines, pyrimidines, and nicotinamide cofactors. This adaptive metabolic regulation was found to be plastic, where GBM adaptively upregulates these metabolic pathways in response to therapy. Restricting alternative carbon sources by modulating the diet diverts GBM metabolism away from biomass production and slows tumor growth. Collectively, these studies represent the first measurements of many metabolic pathways in brain cancer and reveal brain cancer-specific metabolic rewiring that can be selectively targeted by dietary approaches.

[0142] Results

[0143] 13 C glucose infusion ​

[0144] To understand the metabolic fate of glucose in brain tumors, uniformly labeled 13 C-glucose ([U 13 C]-glucose) was infused into mice with intracranial patient-derived xenografts (PDX) of GBM and into patients with suspected GBM undergoing surgical resection. Then, tissues were analyzed by mass spectrometry to determine the accumulation of 13 C from glucose in downstream metabolites ( Figure 6A ). In mice, treatment-resistant luciferase + GFP + PDX (GBM38) from the Mayo Clinic repository was used, and GFP - tumors were isolated from GFP + cortex using fluorescence-guided microdissection. In patients, sample isolation was performed by board-certified neurosurgeons (WNA) using MRI guidance. For glioma patients with tumors in non-functional locations, the surgical practice is to perform a supra-maximal resection, which removes contrast-enhancing tumors, non-enhancing fluid-attenuated inversion recovery (FLAIR) hyperintense tumors, and some surrounding cortex ( Figure 6B ).

[0145] Eight patients participated in this study ( Figure 6C ), of whom 6 were later found to have GBM, one had isocitrate dehydrogenase (IDH)-mutant anaplastic oligodendroglioma, and one had histone H3-mutant G34R grade 4 glioma. Cortical and non-enhancing tumors were obtained from all 8 patients. Enhancing tumors were obtained from only 7 patients because one tumor consisted of completely non-enhancing disease.

[0146] In human patients, [U 13 C]-glucose infusion was continued throughout the craniotomy, typically for about 3 h. Circulating arterial [U 13 C]-glucose levels during surgery ranged between 20 - 40%, and were typically in a steady state after 30 min ( Figure 6D ). The 13 C labeling of arterial lactate (formed by the conversion of infused labeled glucose to lactate in tissues, followed by secretion of lactate into the circulation) varied between patients and was typically between 10 - 30% ( Figure 13A ). As in patient infusions, labeled glucose reached arterial steady state in mice within 30 min, and the total labeled abundance was approximately 50% ( Figure 6D ), while the 13 C labeling of circulating lactate reached approximately 30% ( Figure 13B ).

[0147] Hematoxylin and eosin (H&E) staining was used to confirm the adequate separation of human samples ( Figure 13C ). Tumor content quantification performed by a board-certified neuropathologist (S.V.) indicated that the tumor content in the enhanced tumor samples was approximately 80%, the cortex was 80% in the cortical samples, and it was a mixture in the non-enhanced tumor samples ( Figure 13D ). Consistent with these results, the level of N-acetylaspartate (NAA) in the human cortex was nearly 10-fold higher than that in the enhanced tumors ( Figure 14A ), thus further supporting the adequate surgical separation of the tissues. The absolute levels of many other metabolites were significantly different between the cortical and tumor tissues of mice and patients ( Figure 14B -D).

[0148] Gliomas and cortex have similar glucose carbon incorporation into glycolytic intermediates

[0149] After glucose enters the tissue, glucose is metabolized through glycolysis and the pentose phosphate cycle, enabling its carbon to be used for many downstream fates. Monitoring 13 the incorporation of 13C carbon into the metabolites of these pathways to determine the active pathways in glioma and cortical tissues ( Figure 6E ). In tumor-bearing mice ( Figure 6F ) and humans ( Figure 6G ), the metabolites involved in the upper glycolysis (fructose bisphosphate, GAP / DHAP, phosphoglycerate, PEP) showed similar levels of 13 13C labeling in GBM and cortex, indicating that the labeled glucose reached both tissues adequately and rapidly. Consistent with this finding, UDP-glucose, which is rapidly formed from glucose-1-phosphate and UTP, was similarly labeled in the tumor and non-tumor tissues of mice and patients ( Figure 15A , B).

[0150] Interestingly, in GBM and cortex, the enrichment of lactate and pyruvate was higher than that of the upstream glycolytic intermediates ( Figure 6F , G). These labeling patterns suggest that 13 13C may enter the lower glycolysis through lactate uptake or exchange.

[0151] To complement these LC-MS-based analyses, rapidly frozen tumor tissue sections were also analyzed by matrix-assisted laser desorption / ionization (MALDI) mass spectrometry. This technique has the advantage of analyzing metabolite levels in non-homogenized tissue samples and thus does not require cortex / tumor separation. However, it lacks some of the sensitivity and metabolite identification characteristics of LC-MS. Consistent with the LC-MS results, the glycolytic product lactate had similar 13 13C enrichment in GBM tissue and cortex ( Figure 6H andFigure 16A , B). Collectively, these data indicate that sufficient 13 C glucose enters tumor and cortical tissues during infusion and similarly utilizes / exchanges labeled extracellular lactate.

[0152] Gliomas reduce glucose-driven TCA cycle activity and neurotransmitter biosynthesis

[0153] Using these same samples, metabolites in the TCA cycle were studied, which is a central metabolic hub that allows for the oxidation of glucose-derived carbon and its conversion into other molecules such as neurotransmitters and amino acids ( Figure 7A ). In mouse ( Figure 7B ) and human ( Figure 7D ) cortex, tracer-derived 13 C accounts for approximately 30 - 40% of the TCA cycle intermediates citrate / isocitrate, α-ketoglutarate, succinate, and malate. In contrast, in tumor tissues, 13 C accounts for only 15 - 20% of these TCA cycle metabolites ( Figure 7B ), D). 13 The reduced

[0154] C labeling may indicate a reduced TCA cycle activity in GBM compared to cortex and / or a preferential utilization of non-glucose carbon sources to fuel the TCA cycle. Figure 7C Next, neurotransmitter synthesis was studied. Glucose-derived carbon occupies a large proportion of the neurotransmitters glutamate and γ-aminobutyric acid (GABA) ( 13 ). In both human patients and mouse models, the Figure 7G C labeling of glutamate, glutamine, and GABA in tumor tissues is lower than that in normal cortex, and GABA labeling is almost absent in human GBM ( 13 ). This data indicates that GBM utilizes less glucose to drive neurotransmitter synthesis compared to normal cortex. These measurements were largely confirmed by separate MALDI-based analyses, which similarly revealed a reduction in Figure 7H -I, Figure 16C -F, Figure 17A -C, Figure 18A -C) in the TCA cycle intermediates, glutamate, and glutamine.

[0155] Gliomas increase glucose carbon incorporation into nucleotides

[0156] Although glucose uptake is similar, the contribution of glucose to the TCA cycle and neurotransmitter synthesis is lower. Next, it was determined how GBM preferentially utilizes carbon from glucose sources. The labeling patterns of metabolites from glucose sources were evaluated, which are used by cells as building blocks to synthesize the macromolecules required for cell growth and division.

[0157] Nucleotides and their derivatives include purines and pyrimidines, which are produced by separate metabolic pathways, both of which use ribose 5-phosphate (R5P) from glucose sources generated in the pentose phosphate pathway ( Figure 6E ). Cells can de novo synthesize purines, where carbon and nitrogen from many sources are added to R5P in an energy-intensive process ( Figure 8A ). Alternatively, cells can also salvage nucleotides by conjugating R5P with preformed nucleobases. ( Figure 8A ). Notably, in both mouse models ( Figure 8B ) and human patients ( Figure 8C ), the 13 C labeling of many purine metabolites (including GMP and GDP) is increased in brain cancers relative to the cortex. Since the enrichment of R5P is similar between tissues, the increased 13 C enrichment of purines may be the result of higher synthesis in gliomas ( Figure 19A -B). Similar results were observed using MALDI, which specifically showed increased 13 C labeling of purines in GBM tissues compared to normal cortex ( Figure 8H , 16G). Interestingly, when we evaluated the enrichment patterns of individual patients, we found that only the GMP branch of the purine pathway had consistently higher enrichment in all patients ( Figure 20A -D, 21A-C). This suggests that the production of GMP may be particularly important for gliomas.

[0158] Unlike purine synthesis, pyrimidine production begins with the formation of nucleobases from aspartate and carbamoyl phosphate and then conjugation with R5P, ultimately yielding UMP ( Figure 8D ). UMP can also be salvaged from uridine. UMP can be further metabolized to produce additional pyrimidines. Like purines, in mouse models ( Figure 8E ) and human patients ( Figure 8F ), pyrimidines have elevated 13 C labeling in cancer tissues compared to the cortex.

[0159] In addition to driving nucleotide synthesis, carbon from glucose sources is also used to form the essential cofactors NAD and NADH, both of which can promote the oncogenic phenotype ( Figure 23A ). Consistent with the finding of increased nucleotide labeling in glioma tissues compared to the cortex in mice (Figure 23B ) and human gliomas Figure 8G ) showed elevated labeling of NAD and NADH, indicating increased NAD / NADH synthesis, which can support the increased growth and survival demands of tumors. Collectively, these data demonstrate that gliomas reprogram glucose carbon utilization away from TCA cycle oxidation and neurotransmitter synthesis and redirect it towards the biosynthetic requirements for cancer growth.

[0160] Gliomas increase the flux of nucleotide synthesis and decrease the flux of the oxidative TCA cycle.

[0161] High 13 C enrichment at a single time point does not necessarily mean increased biosynthetic flux. For example, nucleotides formed at a low rate from the infused 13 C source may have a higher 13 C enrichment than nucleotides formed at a faster rate from unlabeled sources. Therefore, a metabolic flux analysis (MFA) method was developed to directly quantify nucleotide synthesis flux from in vivo enrichment data Figure 9A ). This mathematical framework was applied to a patient-derived orthotopic GBM mouse model to determine whether higher GBM nucleotide enrichment corresponded to higher synthetic flux.

[0162] Infusion of [U 13 C]-glucose into orthotopic GBM-bearing mice and harvesting of GBM and normal cortical tissues at multiple time points after infusion for LC-MS analysis to generate time-dependent enrichment profiles for MFA Figure 9A , 24). The time-course enrichment profiles of purine and pyrimidine nucleotides showed an increasing trend throughout the 4-h experiment Figure 24A -B), indicating that isotopic steady states in these pathways had not been reached. To overcome this limitation, an ODE-based MFA model was applied that uses time-course nucleotide mass isotopomer distribution (MID) profiles to solve for flux Figure 9A ). Fifteen reactions in the purine synthesis pathway and three reactions in the pyrimidine synthesis pathway were quantified in GBM and adjacent normal cortical tissues Figure 25A -B, Tables 4-7).

[0163] Using MFA, significant differences in nucleotide synthesis rates between GBM and cortex were observed. In the purine synthesis pathway, GBM had higher de novo synthesis fluxes of IMP and GMP than cortex, accompanied by increased salvage synthesis of IMP and AMP Figure 9B, Table 13-14). The increased synthesis of inosine, guanosine, and GDP in GBM further emphasizes the widespread increase in purine biosynthesis in tumors. Notably, a comparison of total metabolite concentrations in GBM and cortical tissue shows that many purines are present at the same or lower abundances in GBM compared to the cortex ( Figure 24C ), which further emphasizes the increased information that can be obtained from 13 C-MFA compared to metabolite isotope tracing and analysis based on static metabolite levels. Collectively, these results suggest that the higher 13 C enrichment of purines observed in tumors stems from a higher absolute rate of purine synthesis.

[0164] Pyrimidine fluxes also differ between GBM and the cortex. De novo synthesis of UMP is increased approximately 5-fold in GBM compared to the cortex ( Figure 9C and Table 14-15). However, uridine salvage is the major form of pyrimidine synthesis in both GBM and cortical tissue and accounts for greater than 80% of UMP synthesis in both.

[0165] Mouse time-course studies were also used to analyze TCA cycle activity in GBM and the cortex. Pyruvate derived from fully 13 C6-labeled glucose enters the TCA cycle via pyruvate dehydrogenase, forming TCA cycle intermediates with two 13 C atoms (M+2, Figure 7A ). These intermediates can be oxidized through further rounds in the TCA cycle, or they can exit the TCA cycle to drive other metabolic reactions. Intermediates that have undergone multiple rounds of the TCA cycle can contain additional 13 C atoms (M+3 to M+6, M+3 may also result from a single round involving the pyruvate carboxylase reaction, Figure 7A ). In both GBM and the cortex, rapid formation of M+2 TCA cycle intermediates (citrate, succinate, and malate) was observed over time. However, the abundances of M+3 to M+6 TCA cycle intermediates increased steadily over time in the cortex but remained low in GBM ( Figure 9D -E, 26A-B, D-E). Additionally, analysis of the changes in isotopologue distributions at the most recent time points (t = 120 min and t = 240 min) in these studies, where GBM labeling was near steady state, similarly revealed a consistent trend of higher labeling in the cortex compared to GBM ( Figure 9F and Figure 26C , F). These findings suggest a higher oxidative turnover of the TCA cycle in the cortex and a lower degree of oxidation of glucose-derived TCA cycle intermediates in GBM.

[0166] GBM metabolic activity is dynamic after therapy

[0167] GBM is characterized by strong treatment resistance. To determine whether metabolic adaptation promotes the ability to respond to standard-of-care treatments such as RT, GBM-bearing mice were treated with cranial RT delivered to the entire brain (tumor and cortex) immediately (<5 min) before 13 [U-

[0168] C]-glucose infusion and tumors and cortex were harvested over time, as shown in Figure 9. 13 Assume that the initial MFA model (Figure 9) is in a metabolic steady state throughout the infusion. This assumption is unlikely to hold after RT due to the rapid activation of the DNA damage response and subsequent cell cycle arrest. Therefore, a dynamic- Figure 10A [[U-

[0169] C-MFA (DMFA) model was developed to quantify purine synthesis flux ( 13 ) after RT. Figure 10A 、 27A -B, Supplementary Methods). Notably, purine fluxes change dynamically after RT in GBM, but are largely unaffected in cortical tissue ( Figure 10B -I, Figure 28 ). De novo IMP synthesis transiently increases after RT, reaching peak activity at approximately 1 h after RT and gradually decreasing over the next 3 h ( Figure 10C ). Notably, this pattern and time frame of increased de novo IMP synthesis are in perfect agreement with the known time frame of DNA damage and repair after RT. In contrast, IMP salvage from hypoxanthine is unaffected in both GBM and cortex ( Figure 10D ). De novo synthesis of GMP from IMP also increases within approximately 1 h, which is consistent with increased IMP synthesis, and this increase persists for the next 3 h ( Figure 10E ), while both guanosine salvage and de novo AMP synthesis decrease after RT ( Figure 10F -H). The increased AMP salvage partially compensates for the lower de novo AMP synthesis (Figure 10I). Together, these data indicate that after RT, GBM acutely increases de novo IMP synthesis, which leads to increased guanosine production, accompanied by decreased AMP production.

[0170] Gliomas preferentially rely on environmental serine

[0171] De novo purine synthesis requires multiple amino acid substrates, including serine, a neurotransmitter, a driver of lipid synthesis, and a precursor of glycine and one-carbon units. Because serine metabolism is important in various tumors, including GBM, we next investigated whether isotope infusion would help us understand serine metabolism in human brain cancer.

[0172] In both murine ( Figure 11A ) and human ( Figure 11B ) studies, the total 13 C labeling of serine was similar in brain cancer and cortical samples. This finding differed from many other amino acids, neurotransmitters, and nucleotides, which showed different labeling enrichments in brain cancer and cortex (Figures 7, 8). In-depth study of the labeling patterns in murine GBM and cortical tissues revealed that the M+3 labeling of serine was predominant in cortex, while the M+1 labeling was predominant in GBM tissues ( Figure 11C ). A similar labeling pattern was observed in most human tissues, where in almost all cases, M+3 serine was higher in cortex than in enhancing tumors, while in most patients, M+1 serine was predominant in both enhancing and non-enhancing tumor tissues ( Figure 11D , 29A).

[0173] There are multiple potential sources of labeled serine, including (1) de novo synthesis from glucose, (2) uptake from the environment, and (3) synthesis from the addition of carbon from the folate cycle to the two-carbon amino acid glycine. In both murine cortical and GBM tissues, the glycolytic intermediate phosphoglycerate (PG), a precursor of serine, was almost entirely M+3 labeled in both cortex and GBM ( Figure 11E ). As in mice, human PG was predominantly M+3 labeled in all tissues ( Figure 11F ). Thus, any serine formed de novo from glycolytic intermediates would also be predominantly M+3 labeled. The predominance of M+3 serine in cortex and M+1 serine in brain cancer suggests that cortex mainly generates its serine from glucose, while GBM tissues may rely on other sources.

[0174] Potential alternative serine sources in brain cancer were investigated. Arterial serine in both patients and mice was predominantly M+1 labeled ( Figure 11E , F), likely due to the synthesis of unlabeled glycine and labeled folate carbon from the kidney and liver. Thus, a higher dependence on circulating serine uptake may account for the M+1 serine seen in murine and human brain cancer samples. However, another potential source of M+1 is reverse SHMT flux, which can generate M+1 serine through the combination of unlabeled glycine and labeled 1-C units in the folate cycle ( Figure 11G ). Given this complexity, a multi-compartment 13The C-MFA model was used to understand the relative magnitudes of these fluxes in patient tumors ( Figure 11H ). The model includes multiple tissue compartments, all with the same circulating serine source (see Methods). To ensure consistency of results, exogenous serine synthesis / uptake in all compartments was constrained to 1. Figure 11H The resulting scores of de novo serine synthesis flux versus serine uptake flux are depicted in (the calculation of the scores is described in the Methods). Ratios greater than 1 imply a higher contribution of de novo serine synthesis relative to the cortex in the tumor, while ratios less than 1 imply a higher dependence on serine uptake relative to the cortex. In mouse samples, the cortex was mainly dependent on de novo serine synthesis, while GBM samples obtained most of their serine from extracellular sources ( Figure 11H ). Patient samples showed some heterogeneity. While the cortex mainly generated serine de novo, many enhanced (6 out of 7) and non-enhanced (4 out of 8) tumor samples were mainly dependent on extracellular serine uptake ( Figure 11H , 29B). Collectively, these data indicate that, compared to the cortex, in many brain cancers, the relative flux of de novo serine synthesis is lower, and brain cancers obtain serine from the environment.

[0175] This observation suggests that brain cancers shift towards serine uptake and downregulate glucose-driven serine synthesis, enabling them to utilize glucose carbon for biosynthesis and growth instead. To test this hypothesis, environmental serine was restricted by feeding GFP + fluc + GBM-bearing mice a serine-restricted diet (Figure 12). Dietary serine restriction decreased circulating serine levels as expected ( Figure 30A ), and significantly slowed tumor growth as assessed by bioluminescence ( Figure 12A , B). When control mice neared the humane endpoint, the mice were euthanized, and brain and tumor tissues were harvested from all groups for analysis. Tumors in serine-restricted mice were smaller than those in the control group ( Figure 12C ), and had a lower proliferation index as measured by Ki-67 staining ( Figure 12D -E). Metabolite quantification showed that the serine / glycine-restricted diet significantly altered the metabolome of GBM tissues as assessed by principal component analysis, but had little effect on cortical metabolism ( Figure 30B 、 30C ). This observation is consistent with glucose-driven de novo serine synthesis being the major pathway of synthesis in the cortex. GBM samples from mice on a low serine / glycine diet had lower levels of nucleotides, NAD + and NADH compared to GBM samples ( Figure 12F ), but serine levels were only moderately decreased (Figure 12G )。 These findings suggest that when extracellular serine sources are limited, there is a compensatory shift of glucose carbon towards serine within the tumor. Consistent with this hypothesis, in the GBM tissues of mice fed a serine / glycine-restricted diet, the level of phosphoserine (an intermediate formed when glucose carbon is diverted towards serine) was significantly elevated ( Figure 12G ). These data suggest that many brain cancers preferentially rely on extracellular sources of serine but can adapt to serine limitation by slowing proliferation and diverting glucose carbon from biomass production towards serine synthesis ( Figure 12H -J).

[0176] In summary, the experiments in this article have revealed a profound rearrangement of carbon metabolism in invasive human brain cancers, which fuels tumor growth. These cancer-specific metabolic alterations, such as the preference for environmental serine and the dependence on IMPDH for GTP synthesis, are potential therapeutic targets with favorable therapeutic indices.

[0177] Discussion

[0178] Here, a clinically stable isotope tracer procedure was developed and tested that integrates the infusion of [U 13 C with 13 C-MFA to define the metabolic rearrangements occurring in brain cancers and understand their therapeutic implications. While both brain cancers and the cortex consume glucose extensively and engage in glycolysis, the cortex primarily uses glucose-derived carbon for physiological processes such as TCA cycle oxidation and neurotransmitter synthesis. Brain cancers downregulate these physiological processes and instead use glucose-derived carbon to synthesize nucleotides, including NAD + and NADH, to fuel proliferation. By developing a quantitative 13 C-MFA model, upregulated de novo synthesis of purines and pyrimidines in GBM was identified, and there was a strong GBM-specific metabolic response to radiotherapy. Finally, this article demonstrated that the cortex synthesizes a higher proportion of serine from glucose, while brain cancers salvage serine from the environment. This metabolic rearrangement is a targetable vulnerability with a therapeutic window. In a mouse model, dietary serine restriction depleted the GBM nucleotide pool and slowed tumor growth while having minimal impact on cortical metabolism.

[0179] This work provides insights into how human brain cancer metabolism is altered and adds to the growing body of knowledge regarding cancer metabolic rearrangements. The infused [U 13C]-glucose accumulates rapidly in both GBM and the cortex. The findings in this paper suggest that widespread targeting of glucose uptake in an attempt to slow GBM growth is unlikely to have a favorable therapeutic window and may result in adverse toxicities. An active TCA cycle was observed in brain cancer. However, the unique surgical practice in this paper enabled the first comparison of metabolic pathway activities in human cortex and brain cancer. Although the TCA cycle is active in GBM, it appears to be downregulated compared to non-malignant cortex, as evidenced by a preference for non-glucose substrates and a decline in cycle turnover. The pathway of serine synthesis has not been studied in human cancers. Different from brain metastases that seem to rely on de novo serine synthesis in preclinical models, GBM preferentially relies on ambient serine and does so to divert glucose carbon for nucleotide synthesis and proliferation instead.

[0180] described in this paper 13 The C-MFA model provides insights into metabolic rewiring that are difficult to obtain using simpler analytical techniques. Although de novo synthesis of both purines and pyrimidines is increased in GBM compared to the cortex, salvage of uridine and hypoxanthine seems to dominate nucleotide production. This situation seems to be different from other brain tumors, in which de novo synthesis of pyrimidines dominates. These results suggest that targeting upstream steps of de novo nucleotide synthesis in GBM may lack efficacy because compensatory salvage pathways can fill the nucleotide pool when upstream steps are blocked. The flux model in this paper also indicates that GBM adaptively rearranges metabolism in response to radiation, which may explain why these tumors often recur after radiotherapy. Additionally, dynamic 13 C-MFA analysis reveals an increased dependence on de novo GMP synthesis after radiation, highlighting the important role of metabolic flux in treatment response. Some flux models require samples to be collected at multiple time points and are not applicable to clinical applications where tumors are usually removed only once. However, the serine production flux model in this paper only requires a single time point, so this model will have increased applicability in real-world practice. The serine production model makes several simplifying assumptions (described in the supplementary methods) because the ability to increase model complexity depends on the underlying data. This study demonstrates the utility of simplified models in extracting quantitative information from metabolic studies. As experimental techniques develop, these data can be used to develop more complex models.

[0181] This work has several important clinical implications. Inhibiting nucleotide synthesis, serine uptake, or non-glucose TCA cycle energy sources may selectively affect the therapeutic index of GBM, while broad targeting of glucose uptake may lead to unacceptable cortical toxicity. Due to active salvage pathways, targeting proximal nucleotide de novo synthesis in GBM may be ineffective. Blocking IMPDH may still have therapeutic benefits for gliomas, with a favorable therapeutic ratio, as gliomas preferentially salvage hypoxanthine. Limiting dietary serine helps slow the growth of GBM and may increase the efficacy of standard GBM treatments, although the efficacy of this approach may be limited by local serine production in the GBM microenvironment. The observed heterogeneity in environmental serine dependence among patients suggests that isotope tracing can be used as a precision medicine technique to determine which patients are most likely to benefit from dietary serine restriction.

[0182] This study was the first to directly measure biosynthetic fluxes in both glioma and cortical tissues from patients with human brain cancer. Brain tumors reprogram the utilization of glucose carbon from oxidation and neurotransmitter production to biosynthesis for growth. Blocking these metabolic adaptations through dietary intervention can slow the growth of brain cancer while minimally affecting cortical metabolism.

[0183] Methods

[0184] Clinical stable isotope tracer protocol

[0185] Eight patients suspected of having GBM were recruited into an IRB-approved clinical study that was conducted with standard-of-care craniotomy during the perioperative period. Before the start of each surgery (approximately 2 - 4 hours before tissue resection), patients received an intravenous bolus dose of [U 13 C]-glucose (8 g), followed by a continuous intravenous infusion of [U 13 C]-glucose at a rate of 4 g / h. Arterial blood was collected into EDTA-coated vials every 30 - 60 min for plasma preparation and analysis until solid tissue of interest was harvested from each patient. At this point, radiologically defined enhancing tumor, non-enhancing tumor, and adjacent healthy cortical tissue were resected by a neurosurgeon (WNA), rinsed in cold PBS by the study team, and immediately (<3 min after resection) snap-frozen in liquid nitrogen for further analysis.

[0186] Animal studies and patient-derived xenograft models

[0187] All animal studies were approved by the University Committee on Use and Care of Animals at the University of Michigan. In all animal experiments, male and female mice aged 4 - 12 weeks were used. The mice were housed under specific pathogen - free conditions at a temperature of 74°F, with relative humidity between 30% and 70%, a 12h light / 12h dark cycle, and free access to food ( Laboratory Rodent Diet, 5L0D) and water.

[0188] The study evaluating intracranial tumor - bearing mice used the PDX model GBM38, a chemoradiation - resistant model that is genetically and histologically representative of typical GBM, from the PDX National Resource at the Mayo Clinic. Tumor tissue was propagated subcutaneously in the flanks of immunodeficient mice (B6.129S7 - Rag1 tm1Mom / J [Rag1 KO], Jackson Laboratory). To introduce GFP and fluc into GBM tissue, flank tumors were used to generate short - term explant cultures and transduced by lentiviral infection (lenti - LEGO - Ig2 - fluc - IRES - GFP - VSVG). After infection, cells in the GFP + population were enriched by fluorescence - activated cell sorting and then re - introduced into mice as subcutaneous flank tumors or intracranial tumors. To generate orthotopic GBM brain tumors, 5×10 5 GFP + fluc + GBM38 cells were stereotactically implanted into the brain region of the striatum of anesthetized Rag1 KO mice calculated to be. Tumor development was then confirmed by bioluminescence imaging (BLI) as described below.

[0189] Tumor Growth and Bioluminescence

[0190] To monitor the growth of intracranial tumors in mice, BLI was used, which takes advantage of luciferase expression in intracranial tumors. For each measurement, 150 mg / kg D - luciferin was injected intraperitoneally into mice implanted intracranially with fluc + GBM38 cells. Ten minutes after injection, the mice were imaged under anesthesia (inhalation of 2% isoflurane) using an IVIS TM Spectrum imaging system (PerkinElmer). In the tumor growth study, the total flux of each tumor was normalized to the flux at time 0, which was defined as the first day detected after intracranial implantation.

[0191] Stable Isotope Infusion in GBM Tumor-Bearing Mice

[0192] Approximately 1-2 weeks before expected death associated with the brain tumor (~3 weeks post-implantation), intracranial GBM tumor-bearing mice underwent dual catheterization, with one catheter surgically placed into the jugular vein (for [U 13 C]-glucose administration), and another catheter placed into the carotid artery (for plasma collection during infusion). The mice were then allowed to recover from surgery for 4-5 days. In the study evaluating the effect of RT on metabolism, mice intubated under inhalation of 2% isoflurane anesthesia were then treated with cranial-directed RT at a dose of 8 Gy or sham RT with the cranium exposed and shielded with lead. Immediately after RT (<5 min), a bolus dose of [U 13 C]-glucose (0.4 mg / g) was administered to the awake and active mice, followed by a continuous infusion of [U 13 C]-glucose (12 ng / g / min) via an intravenous infusion tube for a total of 4 h. During the infusion, blood was periodically collected into EDTA-coated vials via a lateral neck infusion tube and used for plasma preparation. At the end of the infusion, ketamine (50 mg / kg) was rapidly administered into the intravenous infusion tube to induce anesthesia. The mice were then decapitated, and tissues were harvested on dry ice. To separate in situ GBM from normal mouse cortex, we performed microdissection with the aid of a fluorescent lamp that enabled us to distinguish GFP + tumors from GFP - cortex. Then all tissues were immediately (<3 min post-anesthesia) snap-frozen in liquid nitrogen for further analysis.

[0193] Liquid Chromatography-Mass Spectrometry

[0194] The snap-frozen tissue samples were homogenized in cold (-80 °C) 80% methanol. For plasma analysis, 100% methanol was added to plasma samples at -80 °C to yield a final methanol concentration of 80%. Then insoluble materials were precipitated from all samples by centrifugation at 4 °C, and the supernatant containing soluble metabolites was dried by nitrogen purging. The dried metabolites were then reconstituted in 50% methanol for LC-MS analysis. An Agilent system consisting of an Infinity Lab II UPLC coupled to a 6545 QTOF mass spectrometer (Agilent Technologies, Santa Clara, CA) was used to determine isotope labeling, and data were analyzed using MassHunter Profinder 10.0 with values corrected for natural isotope abundance. We used control samples without 13 C labeling to ensure that from [U 13The labeled isotopologs of mice and patients receiving C]-glucose infusions were not from contaminated samples. To determine the relative metabolite abundances in tissues and plasma of control or Ser / Gly(-)-diet-fed mice, samples were prepared as described above and then analyzed using an Agilent 1290 Infinity II LC-6470 triple quadrupole tandem mass spectrometry system (Agilent Technologies, Santa Clara, CA). Agilent MassHunter Quantitative Analysis software version B.08.02 was used for compound optimization, calibration, and data acquisition.

[0195] MALDI mass spectrometry

[0196] Before matrix coating, standard microscope slides containing tissues were vacuum dried for 20 minutes. After drying, the slides were sprayed with NEDC matrix (10 mg / mL, 1:1 ACN:H2O) using an M3+ sprayer (HTX Technologies LLC, Chapel Hill, North Carolina, flow rate: 75 μL / min, temperature: 70 °C, speed: 1000 mm / min, track spacing: 1 mm, pattern: crisscross, drying time: 0 s). Before analysis, the slides were mounted into an MTP slide adapter II (Bruker Daltonics, Billerica, MA).

[0197] MALDI imaging data were acquired using a timsTOF fleX MALDI-2 mass spectrometer (Bruker Daltonics) operating in transmission mode with a 20-μm raster size, acquiring m / z from 100 - 600. Taurine was used as the lock substance ([M-H]1-, m / z 124.0074).

[0198] The mass spectrometry imaging data was visualized using SCiLS Lab 2023b. In SCiLS Lab, internal scripts utilizing the SCiLS REST API (Bruker Daltonics; version 6.2.114) were used to generate single-stage enrichment fraction images, normalized mean enrichment images, and hierarchical enrichment images. These internal scripts were written in the R language (version 4.2.2) and run using RStudio (2022.12.0 Build 353). The segmentation algorithm built into SCiLS Lab was used to create four data-driven regions corresponding to healthy and GBM tissues in tissues administered with 13 C and control tissues (Normalization: total ion count, Denoising: weak, Method: bisecting k-means, Metric: Manhattan). Another internal script implemented through the SCiLS REST API also calculated the relative isotopologue density of these regions.

[0199] Preliminary annotation was performed using MetaboScape 2023 (Bruker Daltonics), which used a list of known biomolecular targets generated by the TASQ software (Bruker Daltonics; amino acids, glycolysis, citric acid cycle, urea cycle, bile acids, gangliosides) as well as LipidBlast and LIPIDMAPS. The molecular formulas of the target molecules were used to calculate the exact mass of each target. The annotation required a mass error of less than 3.0 ppm. A total of 72 features were annotated using this limited list, and the annotated peaks had a mass accuracy of 1.1 ppm.

[0200] Metabolic flux analysis

[0201] In vivo metabolic flux analysis (iMFA) methods were developed to estimate purine and pyrimidine fluxes from isotopologue time-course data. The steady-state IMM-MFA method was used to estimate the contribution of serine in human brain tumors.

[0202] iMFA in metabolic steady state

[0203] The model parameters include reaction fluxes (represented as vector v), pool sizes of mass balance metabolites (represented as vector c), isotopologues of input metabolites (R), and the contribution ratio of reactant isotopologues to product isotopologues (f) for the pyrimidine model only. The vector x of model parameters is described in Equation 8.

[0204] x = [v, c, f, R]

[0205] Equation 8

[0206] Metabolites within the model boundary are mass balanced and are called balanced metabolites. Metabolites outside the model boundary are not mass balanced and are called input metabolites. Due to the complex time-dependence of metabolite enrichment in the body, this demarcation between input metabolites and balanced metabolites is used to build the model. A set of linear mass balance equations are used to describe the overall mass balance. The sum of the isotopologues of the input metabolites is restricted to 1. Equation 9 describes the linear constraint equation. S is the stoichiometric matrix of a model with m balanced metabolites and n reactions. L is the linear constraint on the sum of the input metabolite isotopologues, corresponding to p labeled input metabolites and r total isotopologues.

[0207]

[0208] The time-dependent fractional isotopologue enrichment (MID) of balanced metabolites is described by a set of ordinary differential equations (ODEs, Equation 10). The rate of change of the isotopologue d(M i,d ) of metabolite i is described by applying mass balance on the isotopologues.

[0209]

[0210] The objective function is minimized to solve the model and estimate the optimal parameters (Equation 11). The objective function (obj) is calculated as the sum of the squares of the differences between the measured values of isotope enrichment (M expt ) and the isotope enrichment simulated by the model (M sim ) divided by the standard deviation (SD expt ) of the experimental measurements. When the metabolite pool size is known, the difference between the known and simulated pool sizes is included in the objective function (c expt -c sim ).

[0211]

[0212] To estimate fluxes and pool sizes, an initial parameter vector is randomly selected and the ODEs are solved to estimate the objective function. The objective function is minimized subject to linear constraints and parameter bounds. Optimization is performed using the Artlelys Knitro toolbox in MATLAB. The solver ode15s is used to solve the initial value problem (IVP) of the ODEs. All metabolites are unlabeled at time t = 0. Optimization is performed on 100 randomly generated initial parameter vectors, and the chi-square goodness-of-fit test is used to select the optimal parameter vector with 95% confidence. When the objective function is higher than the chi-square threshold, the parameter space with the lowest objective value is selected. The 95% confidence interval of the estimated fluxes is determined.

[0213] Dynamic iMFA

[0214] Data on the time-dependent changes in the metabolite pool sizes induced by radiation were incorporated into the model together with the MID-time profiles. The time-course flux profiles were parameterized by representing them as B-splines (Equation 12). A B-spline is a parametric function that can be used to fit data without assuming a functional relationship between the input and output variables. It consists of multiple polynomial segments joined together via “control points”. These control points govern the shape of the B-spline curve and are hyperparameters in the model. Another hyperparameter is the order of the B-spline, which is equal to d + 1, where d is the degree of the polynomial used to construct the B-spline.

[0215] v(t) = CP * N(t)

[0216] Equation 12

[0217] The parameter vector includes the metabolite pool size at time t = 0 (c0), as well as the B-spline parameters and the isotopomers of the input metabolites (R) represented as a vector cp. The rate of change of the metabolite pool size is expressed as a function of the stoichiometric matrix S and the time-dependent flux vector v(t) (Equation 14).

[0218] x = [cp, c0, R]

[0219] Equation 13

[0220]

[0221] The objective function from the steady-state iMFA model was modified to include a term for the time-dependent metabolite pool size (Equation 15). Only the relative time-dependent pool sizes can be measured experimentally. Therefore, the relative change in the metabolite pool size at time t (c t ) with respect to the pool size at time 0 (c0) was used in the objective function. The initial metabolite pool size values were the same as those used in the steady-state model. Figure 22B Relative time-dependent concentration profiles were provided.

[0222]

[0223] To estimate the flux profiles, an initial parameter vector was randomly selected and the ODEs were solved to minimize the objective function, as done for the steady-state model. The flux values at t = 0 were constrained within the 95% confidence interval estimated by the steady-state model. All metabolites were unlabeled at time t = 0. Optimization was performed on 100 randomly generated initial parameter vectors, and the parameter vector with the lowest objective value was selected. To estimate the 95% confidence interval, the parameter bounds were estimated to be the same as those of the steady-state model. The determined parameter bounds were used to create time-course flux profiles corresponding to the 95% confidence interval. All acceptable flux profiles were recorded, and the minimum and maximum flux values at a given time were reported as the 95% flux bounds.

[0224] B-spline hyperparameter selection was performed prior to parameter optimization. Second-, third-, and fourth-order B-splines were tested, and the third-order spline (quadratic B-spline) was selected after qualitative analysis of the results. A random method was applied to select the B-spline control points. It was assumed that all flux profiles had the same control points. Control points in the range [0.2, 0.8] were tested at intervals of 0.05. Each time a position was selected, parameter optimization was performed on the same initial parameter vector. The control point with the lowest objective was recorded. To optimize the position of the second control point, the same strategy was used. The second control point was placed at a position at least 0.2 away from the first control point. This process was repeated for 100 initial guesses. For GBM and normal cortex samples, adding a second control point did not reduce the minimum objective value for 100 optimizations. Therefore, one control point was used to simulate both conditions. Based on model fitting, 0.3 was selected as the control point for GBM because of the lower average objective value and central position. For normal cortex, 0.65 was selected.

[0225] Metabolic model of the purine pathway

[0226] The metabolic model of the purine synthesis pathway was established based on experimental data and existing literature. The KEGG database was referenced to obtain a list of reactions and related enzymes (Kanehisa, M. and Goto, S. (2000) KEGG: kyoto encyclopedia of genes and genomes. Nucleic Acids Res 28, 27-30). Data from the Human Protein Atlas were used to remove reactions with low enzyme expression in GBM (Sjostedt, E. et al. (2020) An atlas of the protein-coding genes in the human, pig, and mouse brain. Science 367). All reactions were assumed to be unidirectional and further simplified based on existing experimental data. The net flux was assumed to be in the direction of purine synthesis. In addition, it was assumed that IMP directly produces GMP, and the intermediate XMP was excluded from the model because there was no enrichment data for XMP. It was assumed that all ribose units (R5P, R1P, PRPP) had the same enrichment. The final model included 15 reactions and 23 metabolites ( Figure 25A , Tables 4, 5). Six purine metabolites were within the model boundary and mass balanced. The remaining metabolites were substrates in the purine pathway and outside the model boundary. Based on experimental data, it was assumed that the metabolites adenosine and hypoxanthine were not labeled. Enrichment data for guanine were not available, and it was assumed that it was mainly produced by the degradation of old DNA and RNA units and was therefore not labeled in the model. It was assumed that the cellular carbon dioxide pool was not labeled. The enrichment of methyl units could not be measured experimentally, and these values were estimated from the enrichment of serine and glycine.

[0227] Table 4: List of model reactions and related flux boundaries.

[0228]

[0229]

[0230] The reaction type irreversible refers to a reaction that proceeds in only one direction. The reaction type sink refers to a reaction that consumes metabolites and is not included in the model. Flux boundaries were set according to experimental data. AMP: adenosine monophosphate; C-THF: 5-methyltetrahydrofolate; CO2: carbon dioxide; GLY: glycine; IMP: inosine monophosphate; GDP: guanosine diphosphate; GMP: guanosine monophosphate; R5P: ribose-5-phosphate

[0231] Table 5: List of metabolites included in the model.

[0232]

[0233] The input metabolites are not mass balanced. Some input metabolites have zero to low isotopic enrichment and are considered unlabeled.

[0234] To estimate the methyl unit enrichment, a pseudo-steady state assumption was employed. The serine, glycine, and methyl enrichments were assumed to be in equilibrium at any given time. The corresponding equations for metabolite isotopologues are shown in Table 6 (SER: serine; GLY: glycine; ME: ME-THF; the numbers in the subscripts correspond to the presence (1) or absence (0) of 13 C carbon at that position). The variance-weighted sum-of-squared residuals between the experimental MID values and the model estimates for serine and glycine were calculated. Optimization was carried out from 10 initial guesses. To estimate the error in the estimated methyl enrichment, Gaussian noise was added to the experimental values and the optimization was repeated 200 times.

[0235] Table 6: Equations for estimating methyl unit enrichment

[0236] S.No. Equation 1 <![CDATA[SER 000 = GLY 00 ME0]]> 2 <![CDATA[SER 001 = GLY 00 ME1]]> 3 <![CDATA[SER 100+010 = GLY 10+01 ME0]]> 4 <![CDATA[SER 101+011 = GLY 10+01 ME1]]> 5 <![CDATA[SER 110 = GLY 11 ME0]]> 6 <![CDATA[SER 111 = GLY 11 ME1]]> 7 <![CDATA[ME0 + ME1 = 1]]>

[0237] Metabolic model of the pyrimidine pathway

[0238] The pyrimidine model was implemented based on: the pyrimidine enrichment data available to us, the active reactions in the KEGG database, and the enzymes highly expressed in GBM by examining the Human Protein Atlas. The pyrimidine model consists of three reactions, which are assumed to be unidirectional reactions for the synthesis of UMP and are listed in Table 7 and described in Figure 25B . The flux boundaries were selected based on our observations of the optimization space and relaxed to have no overlap with the flux confidence intervals.

[0239] Table 7: List of pyrimidine model reactions and associated flux boundaries.

[0240]

[0241] The reaction type irreversible refers to a reaction that proceeds in only one direction. The reaction type sink refers to a reaction that consumes metabolites and is not included in the model. The flux boundaries were set according to the experimental data. UMP: uridine monophosphate; CO2: carbon dioxide; R5P: ribose-5-phosphate; ASP: aspartic acid.

[0242] Table 8: List of metabolites included in the pyrimidine model.

[0243]

[0244] The input metabolites are not mass balanced. Some input metabolites have zero to low isotope enrichments and are considered unlabeled.

[0245] The input metabolites for the model include R5P, aspartate, CO2, and uridine (Table 8). We assume that all ribose units, including R5P, PRPP, and R1P, have the same enrichment profile. The only metabolite in the model is UMP, and we establish a mass isotopomer balance for it (Equation 16).

[0246]

[0247] On the left side of Equation 16, the rate of change of the UMP isotopomers is calculated. c UMP represents the concentration of UMP. The first term shows that UMP obtains labeling from the salvage flux (v 尿苷，i where i represents the M+i enrichment) through uridine MID (M 补救 ). The second term shows that UMP obtains labeling from the de novo flux of UMP (v R5P，j ) through R5P (M ) and aspartate 从头 MID. In this model, CO2 is assumed to be unlabeled. The UMP produced in de novo synthesis consists of nine carbons, five of which come from R5P to form the ribose unit of UMP. The remaining four carbons in the uracil ring come from the unlabeled CO2 pool (position 2) and aspartate (positions 4, 5, and 6). UMP de novo synthesis is a decarboxylation reaction, and if the first carbon of aspartate is labeled, the carbon leaving the system as CO2 may be labeled. Therefore, we define a new isotopomer distribution for aspartate that only contributes to UMP labeling. Table 9 shows the aspartate isotopologues corresponding to each isotopomer of aspartate (M ASP，M+i ) that can enrich UMP in the same way. For this purpose, three isotopologue fractions (f1, f2, f3) are defined. For example, assume that one labeled carbon in UMP comes from aspartate Since the labeling of the first carbon of aspartate does not affect the labeling of UMP, the following isotopologues of aspartate can produce one labeled carbon in UMP: 0001, 0010, 0100, 1001, 1010, and 1100. The fraction f iHelp us separate isotopologues into isotopologues with labeled produced CO2 and unlabeled produced CO2. For example, f1 is the ratio of the isotopologue 1000 to all isotopologues of M+1 (0001, 0010, 0100, 1000). To limit the lower and upper boundaries of the fractions, we used the isotopologue distributions in mouse and human tumors reported in reference

[10] . Thus, we set the constraints for f1, f2, and f3 to [0.1, 0.4], [0.2, 0.6], and [0, 1], respectively. To combine the probabilities of producing UMP M+i isotopologues from aspartate and R5P, we multiply the M+j of R5P (M R5P，j ) by the newly defined aspartate isotopologue where j + k = i. The third term in Equation 16 represents the consumption of UMP in other reactions outside the model boundaries or in the total UMP synthesis.

[0248] Table 9: Contribution of aspartate labeling to UMP labeling.

[0249]

[0250] Metabolite pool size

[0251] When available, the purine and pyrimidine pool sizes of the mouse brain were obtained from the literature. Only the values reported with the measurement standard deviation were included in the objective function. When the measurement error was not available, the reported values were only used to set the boundaries of the corresponding pool size parameters. Experimental data were used to estimate the pool sizes of GBM tissues. The average relative metabolite ion numbers between GBM and brain tissues were calculated and multiplied by the pool sizes in the brain. The standard error propagation technique was used to estimate the standard deviation of the GBM pool sizes. GMP was not detected in brain tissues but was detected in GBM tissues. Therefore, the boundaries of the GMP concentration were set to be higher than the pool sizes in the brain. The pool size data and the source literature are shown in Table 10.

[0252] Table 10: Purine and pyrimidine pool sizes used in the metabolic model.

[0253]

[0254] Enrichment of input metabolites

[0255] Applying the metabolic model requires the time-course isotopologue abundances of the input metabolites. In the in vivo model, the time-course enrichment of metabolites is complex and cannot be described by an exact mathematical function. The experimental time point data were fitted with a linear piecewise function to estimate the enrichment-time relationship of the input metabolites. Equation 17 describes the isotopologue R m+1 at time point t m and t iCalculation of the slope. The linear function was chosen because it requires the fewest assumptions and does not overfit the data. Given the uncertainty in experimental measurements, the input isotopologue abundances were allowed to vary within one standard deviation of the experimental measurement mean.

[0256]

[0257] MFA of serine contribution in human tumors

[0258] The model includes three compartments corresponding to cortex, enhanced tumor, and non-enhanced tumor ( Figure 6H ). Each compartment has its own 3PG pool, which is used for de novo serine synthesis within the compartment. These compartments are connected by a common input of exogenous serine from the circulation. Since serine may be derived from proteolysis, an unlabeled serine source is included in the model. Autophagy has been shown to be a source of serine in in vitro models of glioma

[16] . In addition, the rate of de novo serine synthesis is limited by the level of the PHGDH enzyme, and serine may not be in isotopic equilibrium with 3PG. The unlabeled serine source helps to correct for this effect. The net serine input to the model from de novo synthesis, exogenous serine uptake, and unlabeled serine from recycling is assumed to be 1 unit. Forward and reverse SHMT fluxes and the flux of glycine to 5,10-methylene-THF are included in each compartment. Serine is assumed to be the sole source of glycine and one-carbon units. This is consistent with the fact that glycine in the brain is mainly derived from serine. Serine is also the main source of glycine and one-carbon units in glioma. The enrichment of exogenous available serine is also assumed to be the same as that of serine in the circulation. In addition, we assume that the tissue is homogeneous and do not consider any intercellular metabolic interactions in the serine-glycine pathway. These assumptions are very important for reducing model complexity and preventing the model from becoming highly uncertain. Due to various unknown factors, we only analyzed and reported the relative contributions of serine synthesis and uptake pathways that produce labeled serine, and did not analyze absolute values. Sink fluxes of serine, glycine, and formyl-THF are also included to account for consumption not included in the model. Table 11 provides a list of reactions and related carbon transformations.

[0259] The model parameters x include the fluxes v and the known IDV values D of 2PG / 3PG, serine, and glycine in the three compartments. The MID of plasma serine is also included in the model parameters (Equation 18). The fluxes in each compartment are mass balanced, which is achieved through the stoichiometric matrix S corresponding to m metabolites and n reactions m×nis described (Equation 19). External serine is not included in the mass balance. To ensure that the sum of all IDVs for a certain metabolite is always equal to 1, the sum of the IDVs of external serine and 3PG in the three tissues is restricted to 1. This adds 4 equations to the model (one for external serine and 3 for 3PG in the three tissue compartments). These equations are represented by the matrix L corresponding to the d total IDV values in the model. 4×d The three equations that restrict the new serine input to 1 are also included in the linear balance equations and are represented by the matrix N. 3×n

[0260] x = [v, D]

[0261] Equation 18

[0262]

[0263] Isotope mass balance equations (Equation 20) are established using the IMM method (Schmidt, K. et al. (1997) Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices. Biotechnol Bioeng 55, 831 - 840). These equations are used to add non - linear constraints to the model. Additional linear constraints are applied to avoid the model converging to meaningless solutions. The parameters are optimized to minimize the objective function, which is defined as minimizing the difference between the experimentally measured MID and the MID simulated by the model (Equation 21). The difference between the experimental and simulated values is normalized by the experimental standard deviation to account for experimental variation. An L2 regularization term for the flux parameters is also included in the objective function because the model is under - determined, i.e., we have more unknown parameters than the number of known values. The value of the regularization parameter is set to 0.1. To solve the model, local optimization is performed from 200 randomly selected initial points. Optimization is carried out using the Knitro toolbox in MATLAB. The solution with the lowest objective value is selected. To estimate the 95% confidence interval, Gaussian noise is added to the experimental data and the optimization is repeated 1000 times. The distribution of the resulting solutions is used to determine the confidence interval.

[0264]

[0265] Table 11: List of reactions in the MFA model.

[0266] SER: Serine; GLY: Glycine; 3PG: 3 - phosphoglycerate; Me - THF: 5,10 - methylene - THF

[0267] ​

[0268]

[0269] Table 12: Estimated purine fluxes in GBM tissues. Flux bounds represent 95% confidence intervals.

[0270]

[0271]

[0272] Table 13: Estimated purine fluxes in normal cortical tissues. Flux bounds represent 95% confidence intervals.

[0273]

[0274] Table 14: Estimated pyrimidine fluxes in GBM tissues. Flux bounds represent 95% confidence intervals.

[0275]

[0276] Table 15: Estimated pyrimidine fluxes in normal cortical tissues. Flux bounds represent 95% confidence intervals.

[0277]

[0278] Scoring of de novo serine synthesis relative to cortex

[0279] Define a score to compare relative serine synthesis and uptake between cortical and tumor tissues. The ratio of de novo serine synthesis to serine uptake was estimated for each tissue, along with the 95% confidence interval of that ratio ( Figure 25B ). The score was then estimated by dividing the ratio for tumor tissue by the ratio for the matched cortical tissue.

[0280] Dietary restriction of serine and glycine

[0281] Three days prior to intracranial tumor implantation, mice were placed on a control diet containing 1.00% serine and 0.99% glycine ( Baker amino acid diet, 5CC7) or a modified diet ( Modified Baker amino acid diet, in 5BJX), the modified diet contains 0% serine and 0% glycine and is adjusted for all other amino acids to account for the reduced amounts of serine and glycine. Then, intracranial tumors were implanted into the mice, and their respective diets were maintained for the remainder of the experiment. Tumor growth was detected by BLI. Once the control mice were approaching the humane endpoint, the mice were deeply anesthetized, and blood was collected by cardiac puncture into EDTA-coated vials for plasma preparation. Then the mice were decapitated, and the brain was bisected through the tumor tissue. One half of the brain was fixed and embedded for histopathological analysis. As described above, rapid separation of the tumor and cortex based on GFP + was performed on the other half of the brain. Then the tissues were rapidly harvested on dry ice and snap-frozen in liquid nitrogen for metabolomics analysis by LC-MS on an Agilent 6470 mass spectrometer as described above.

[0282] Statistical analysis of metabolite enrichment

[0283] Statistical analysis was performed in R or GraphPad Prism. The data were tested for normal distribution using the D'Agostino normality test (n >= 8) or the Shapiro-Wilk normality test (n < 7). For normally distributed data, a t-test was used for two groups, and one-way ANOVA followed by Tukey HSD was used for more than two groups. For non-normal data, the Mann-Whitney U test was used for two groups. For multiple groups, the Kruskal-Wallis test was used, followed by pairwise comparisons using the Mann-Whitney U test with Bonferroni correction. To reduce the chance of false positives in the differential enrichment analysis, FDR correction was used.

[0284] Example 4

[0285] Glioblastoma multiforme (GBM) is the most common and aggressive primary brain tumor, characterized by severe invasiveness and treatment resistance. The standard treatment course for GBM requires surgical resection, followed by radiotherapy (RT) and temozolomide chemotherapy. Despite current treatments, GBM often recurs, and most patients die within 1 - 2 years of diagnosis.

[0286] Cancer cells have metabolic alterations that provide them with sources of both conventional and unconventional nutrients. They utilize these nutrients to generate new biomass to support their proliferation. This metabolic reprogramming represents a targetable vulnerability with a therapeutic window.

[0287] One way to study cancer metabolism is isotope tracing. By using mass spectrometry to track these isotopes to their downstream metabolites, it is possible to determine which metabolic pathways are active in the system.

[0288] U13C-glucose was administered to GBM patients and GBM patient-derived xenografts (PDX), and higher purine and pyrimidine synthesis was observed in glioma samples, which is consistent with their need for nucleotides to maintain their regulated proliferation. Nucleotide synthesis consists of the salvage pathway and de novo synthesis. In the salvage pathway, free bases react with phosphoribosyl pyrophosphate (PRPP), and in de novo synthesis, carbon and nitrogen from many sources combine with PRPP. Understanding the level of contribution of these pathways to nucleotide synthesis is beneficial because if de novo synthesis is the major source of nucleotide synthesis, drugs targeting de novo reactions, such as mycophenolate mofetil (MMF) or 5-fluorouracil, can be effectively applied. However, because all of these pathways generate labeled metabolites, enrichment data alone cannot be used to determine whether purines are generated via the de novo pathway or the salvage pathway. Therefore, quantification of salvage and de novo synthesis fluxes is beneficial.

[0289] Quantification of metabolic fluxes can be performed using metabolic flux analysis (MFA) that utilizes enrichment data at steady state or isotope non-steady state MFA (INST-MFA) that utilizes time-course enrichment data. In this article, U13C-glucose was infused into patients during craniotomy, which typically takes 2 - 4 hours. Patient enrichment data for purines cannot be used for conventional MFA methods to quantify salvage and de novo synthesis because the enrichment is at a single time point, and purine metabolism is slow, and the enrichment of purines during surgery cannot reach a steady state.

[0290] Enrichment data show that among all nucleotides, guanosine monophosphate (GMP) is the only metabolite that has significantly higher enrichment in all glioma samples compared to normal cortex in patients and PDX. This indicates that the synthesis of GMP is crucial for the proliferation of gliomas. Determining the level of contribution of the salvage and de novo pathways to GMP synthesis is of interest. The drug MMF inhibits the enzyme IMPDH (inosine monophosphate dehydrogenase), which catalyzes de novo synthesis of GMP. Therefore, if GMP is mainly produced by de novo synthesis in patients, MMF can be administered to treat the patient. Otherwise, MMF may be of no benefit to the patient.

[0291] To estimate the contribution of de novo GMP synthesis to overall GMP synthesis, a machine learning model was implemented. Machine learning-based models have two main advantages in estimating flux contributions: (1) Machine learning can identify complex patterns that may be missed by traditional methods. Thus, machine learning can identify structures in enrichment data to estimate pathway contributions from enrichment patterns at a single time point. (2) Compared to mathematical MFA models that require more time and expertise to implement, machine learning models are easier and faster to implement. (3) Once the machine learning model is trained, the predicted response is rapid, and it can be used by clinicians to suggest personalized treatments. Therefore, a machine learning framework was established to indicate which patients may benefit most from targeting the de novo GMP pathway by quantifying the contribution of de novo GMP synthesis to total GMP synthesis.

[0292] An overview of the method is presented in Figure 31 as shown. To train a machine learning model that can predict the ratio of de novo GMP synthesis to overall GMP synthesis, simulated MIDs were used as input features. The data was split into training, validation, and test datasets. The training and validation datasets were used to train the data and evaluate the model performance for each epoch. Additionally, the validation dataset was used to tune the hyperparameters of the model. The criterion we used in hyperparameter tuning was the coefficient of determination (CD) between the actual and predicted values of the validation dataset using Bayesian optimization (BO). The test dataset was used to provide an unbiased evaluation of the final model fit to unknown data. A machine learning model with a good evaluation score on the test dataset should also be evaluated on some experimental values for further validation. The designed experiment consisted of two conditions: a GBM PDX control cohort and GBM PDX treated with MMF. The PDXs were infused with U13C-glucose, and plasma and tissue samples were collected at multiple time points. By measuring the MIDs in these two groups, the de novo GMP ratio could be calculated using the INST-MFA method and compared with the machine learning results. Intuitively, the INST-MFA method should result in a lower de novo GMP ratio in the MMF-treated cohort. After experimental validation, the machine learning model could be applied to patients. Both patient MIDs and scRNA-seq data were available for the experiments in this article. The de novo GMP ratio could be calculated via flux balance analysis and compared with our machine learning results. This method could be applied to clinical trials where machine learning predicts which patients may benefit from MMF treatment.

[0293] Simulating mass isotopomers and flux distributions to train machine learning

[0294] This work uses simulations of mass isotopologues and flux distributions, partly because supervised machine learning requires features of many samples and their corresponding targets; and partly because patient samples are limited and the fluxes (i.e., targets) are unknown. The framework for data simulation is shown in Figure 31 . To simulate purine MIDs and fluxes, a metabolic model including metabolites upstream of de novo purine production was used. The metabolic model enforces fluxes to follow stoichiometric mass balance. It is assumed that fluxes and pools are in a steady state, while MIDs are not. The ratio of de novo GMP synthesis to total GMP synthesis (i.e., the target of the machine learning model) was set to a uniform distribution within the range [0,1], which helps the machine learning model to learn this prediction with the same frequency. A non-linear optimization problem was defined to simulate the stochastic fluxes of mass balance (Eq. 22). To solve this initial value problem, a group of randomly generated uniform fluxes and pools were generated in each iteration. The previous INST-MFA of metabolite enrichments over time-course in GBM PDX was able to determine the fluxes of purine metabolism. The de novo and salvage fluxes of serine were determined using MFA, the enrichments of patient plasma samples over time-course, and a multi-compartment model of cortex, non-enhanced, and enhanced tumors. To limit the fluxes and constrain the distribution of the initial values of fluxes in our optimization, flux boundaries were set based on INST-MFA and MFA fluxes.

[0295] ScRNA-seq of patients and flux balance analysis of patients can be used to further validate the flux boundaries. The optimization problem was solved using the fmincon function in MATLAB. By solving the optimization problem, the group of constrained fluxes for each iteration was calculated.

[0296]

[0297] s.t. S.v = 0

[0298]

[0299] lb ≤ v ≤ ub

[0300] Then, for each set of fluxes, the time-course MIDs were simulated by writing the mass balance for isotopologues and isotomers (Eqs. 23 and 24) and solving the system of ordinary differential equations (ODEs). This process was repeated 50,000 times to generate sufficient samples for machine learning training.

[0301]

[0302] In Eq. 23, the rate of change of the isotopologue d(M i，d ) of metabolite i is from the isotopologues of other metabolites that produce M i，d and the consumption of M i，dCalculated for the isotopologues (second item). Note that if the metabolic model only contains concentration reactions, i.e., there is only one product for each reaction, Eq. 23 can be used. For cleavage reactions, use the contribution of the isotopologue pattern in the mass balance equation (Eq. 24).

[0303]

[0304] Here, the rate of change of the isotopologue vector i(M i ) is expressed as a function of the reaction fluxes v, the stoichiometric matrix S, and the metabolite concentrations c i . The reaction that produces or consumes metabolite i is denoted by j. The index k refers to the metabolite that is converted to i. M k is the isotopologue vector of k, and the atomic transition from k to i is represented by the matrix IMM k→i .

[0305] Metabolic model

[0306] In the flux simulation, a metabolic map consisting of glycolysis, the pentose phosphate pathway (PPP), serine metabolism, and purine metabolism was adopted ( Figure 32A ). Some metabolites were added to the metabolic model to cover patient MID and different compartments. They include the enrichments of plasma glucose and serine (GLCx and SERx) as input metabolites. It is assumed that plasma glucose has an enrichment pattern of M+0 or M+6.

[0307] The enrichment of M+6 glucose was estimated using Eq. 25 [1].

[0308]

[0309] where, GLC M+6，st.st.is the steady-state value of M+6 glucose in plasma and is selected based on the patient plasma enrichment within the range of [0.2, 0.45]. Q is the total amount of glucose in the body and is randomly set to a value between 3g and 7g, which is the physiological range of a human (fasting glucose concentration is 72 - 108 mg / dL, and the average person has 5.5 L of blood) [2 - 4]. r and P are the rate and bolus dose of glucose infusion, respectively. In our experiment, r is 4g / hr and P is 8g. Based on our patient plasma enrichment, it is assumed that plasma serine has M+0 and M+1 labels. It is assumed that M+1 serine exists in the form of the 001 isomer. It is assumed that serine M+1 is in a steady state and is assigned a randomly selected value between 0.2 and 0.65 based on our patient plasma enrichment. Additionally, astrocyte lactate (LACa) is another metabolite added to the metabolic model. Astrocytes are key regulators of central carbon metabolism and are known to have a high conversion rate of glucose to lactate. Astrocytes secrete lactate into the extracellular environment where it can be utilized by other cell types. The described metabolic model is used to constrain the random fluxes (Eq. 22). The stoichiometric constraints defined by this metabolic model change the distribution of the random fluxes from a uniform distribution to a unique distribution controlled by the mass conservation rule ( Figure 32B ). The ODE system consisting of the isotope isomer mass balance (Eq. 24) is solved for the estimated time-course isotope isomers of the metabolites in glycolysis, serine metabolism, and PPP, as shown in Figure 32A . The input metabolites for purine metabolism from other pathways are ribose 5-phosphate (R5P), CO2, 10-formyltetrahydrofolate (MTHF), and glycine (GLY). The MIDs of these metabolites are calculated by summing the isotope isomers that contribute to the isotopologues. Then, another ODE system (Eq. 23) describing the isotopologue mass balance for purine metabolites is solved.

[0310] Data processing of the machine learning model

[0311] Although the simulated data includes many metabolites from glycolysis, serine metabolism, and PPP, only the purine metabolites (IMP, GMP, guanosine diphosphate (GDP)) and R5P are retained to configure the input data with M+1 to M+5 labels. Additionally, since these metabolites produce / consume GMP, they directly affect the de novo GMP ratio. The shape of the simulated data is shown in Fig. 32C, where each row represents the MIDs (i j ) of different metabolites (M k ) at multiple time points (t m ) in one simulation of a group with fluxes (Sim n); where n is the number of MIDs, m is the number of metabolites, k is the number of time points, and j is the number of simulations. A small number of simulations included negative MIDs and infeasible solutions to the flux optimization problem and were thus removed. Through random sampling in the simulations, the data were divided into an 85% training data set and a 15% test data set. The data were normalized according to the mean and standard deviation of the training data. In this way, we reduced the impact of the temporal variation of MIDs on our steady-state targets. The training data were further divided into an 85% training data set and a 15% validation data set. The data were divided into features and targets (the ratio of de novo GMP synthesis).

[0312] Convolutional neural network (CNN) design

[0313] The input features were reshaped into a 4-dimensional (4-D) matrix (number of samples in each data set * k, m, n, 1). The input layer of the CNN shown in Fig. 32D was configured as (m, n, 1) based on the shape of the input data. After the input layer was a 2-D convolutional layer (Conv2D) with a kernel size of (m, 1), resulting in a (1, n) output. The convolutional kernel of the Conv1D layer applied to this output had a size of (n,), thus resulting in a single value. The flatten layer flattened these values in all convolutional kernels and fed them into a fully connected network with two dense layers. The theoretical basis behind this network is that Conv2D captures the dependencies between different metabolites with the same MID, while Conv1D captures the total label.

[0314] Another CNN was also implemented based on the reactions including purine metabolites and R5P (Fig. 32E). The input features were reshaped into a 4-D matrix (number of samples in each data set * k, number of reactions including M m * 2, n, 1). The theoretical basis behind this model is to capture the relationship between the labels of reactants and products. Since there are three reactions directly affecting the GMP label and there is one reactant and one labeled product in these reactions, we configured the shape of the first layer as (number of reactions * 2, n, 1). A Conv2D layer with a kernel size of (2, 1) and a stride of (2, 1) was applied to the input layer, resulting in a (number of reactions, n, 1) output. This output describes the reactions that produce / consume GMP, followed by another Conv2D layer that captures the relationship between GMP-producing reactions and GMP-consuming reactions. The output of this layer entered a Conv1D layer to capture the total label. Then, the flatten layer provided a suitable form of the Conv1D output to enter the dense layer. Compared with the CNN model shown in Fig. 32D, one structural advantage of the CNN model shown in Fig. 32E is that it has fewer trainable parameters because it has more convolutional layers and fewer dense layers.

[0315] To train a CNN, trainable parameters such as the weights of the layers must be optimized to minimize the loss function. The convolutional layer consists of convolutional kernels with trainable weights that are cross-correlated with the output of the previous layer. Using an Adam optimizer with a learning rate of 0.004 and ε of 0.4, a mini batch gradient descent approach with a size of 256 is selected to update all weights according to the gradient of the loss function. Since the GMP de novo ratio is a continuous variable, a regression model is needed to predict it. Therefore, the loss function is set to the mean squared error (MSE). For all layers, the bias term, ReLU activation function, L2 kernel regularizer, and He Uniform kernel initializer are not considered. A batch normalization layer is applied after each activation function. These functions are utilized from the TensorFlow Keras library in python.

[0316] Graph Neural Network (GNN) Design

[0317] Another machine learning model applicable to the reaction network is the graph neural network (GNN). The data processing of GNN is similar to that of CNN, but there are three differences: (1) The simulated MIDs of 7 metabolites including R5P, inosine (INO), IMP, GMP, GDP, adenosine monophosphate (AMP), and guanosine (GUO) are retained; (2) The features are reshaped into a 3-D matrix (the number of samples in each dataset * k, m, n); (3) The input data must be in the graph format with defined nodes and edges. To customize the 3-D matrix of features into a directed graph, the network of metabolites is established as nodes. If the reaction A → B exists, a directed edge from node B to node A is added. The NetworkX library in python is used to construct the graph in Figure 32F and determine the graph adjacency matrix. The logic behind this graph structure is based on the mass isotopomer balance. For example, the isotopomer mass balance for GMP is shown in Eq. 26, where the rate of change of GMP M+i is shown on the left side. On the right side, the first two terms show the production of GMP M+i, while the third term shows the consumption of GMP M+i. To generalize Eq. 26 to the graph, we add a directed edge from GMP to IMP and R5P, as well as a self-loop on GMP for the GMP consumption term.

[0318]

[0319] To create the training, validation, and test graphs, the Spektral library in Python is used, where the 3-D matrix of features is reconstructed into a number of samples * k graphs, where m nodes are connected according to a predefined adjacency matrix, and each node has n features (M+1 to M+5). Based on Eq. 27, mini-batch gradient descent is managed to update the node embedding. In Eq. 27, H (l) is the updated node embedding, A is the adjacency matrix of shape (m, m), and H (l-1) is the previous node embedding of shape (m, n), W (l) represents the trainable weights of shape (n, n), and σ is the activation function.

[0320] H (l) = σ(AH (l-1) W (l) ) Eq. (27)

[0321] The advantage of GNN over CNN is that the convolutional kernel in CNN has a constant shape, but in GNN, node connectivity can be defined with an adjacency matrix. One metabolite may have a degree of one, while another may have a degree of ten; thus, a CNN with a constant convolutional kernel shape cannot cross-correlate with the MIDs of a broader metabolic network, and it is only possible with GNN to make the metabolic connectivity similar.

[0322] Since there is at most 2-hop connectivity in the proposed graph, GNN can benefit from one or two message-passing layers (Figure 32G). The prediction of GMP de novo synthesis is a graph-level regression task, so pooling layers such as GlobalSumPool are used to flatten the graph convolutional output, which can be input into a fully connected layer to predict the ratio of GMP de novo synthesis to total synthesis.

[0323] Hyperparameter Tuning

[0324] Using the Optuna library in Python, Bayesian optimization is used to tune the hyperparameters of the machine learning model. These hyperparameters include the number of neurons in the dense layer, the number of dense layers, the number of filters in the convolutional layer, and Adam optimizer hyperparameters such as the learning rate and ε. In each trial of different hyperparameter combinations, the model is trained and evaluated on the validation dataset. Bayesian optimization has a surrogate function that helps it converge to the best set of hyperparameters faster by skipping some hyperparameter combinations. The Bayesian model attempts to maximize the coefficient of determination between the predictions and actual labels of the validation dataset.

[0325] Results

[0326] The model was evaluated on training and test datasets, and similar correct prediction rates were seen, indicating that the model was not overfitting and was generalizable to unseen data. Figure 33A ) To validate the machine learning model, GBMs were grown in PDXs, some were treated with MMF, U13C glucose was infused, and metabolite enrichment patterns were measured under both conditions. Since MMF targets the IMPDH enzyme or de novo GMP synthesis, a lower de novo GMP synthesis ratio was expected in MMF-treated mice. Consistent with this, the machine learning model predicted a lower de novo GMP synthesis ratio in MMF-treated mice. Figure 33B ) The de novo GMP synthesis ratio in patient tumors was then predicted. Figure 33C ) Enhanced and non-enhanced tumor samples were classified based on their histology in contrast imaging. Non-enhanced tumors had lower vascular penetration than enhanced tumors. The model predicted nearly identical results in patients comparing enhanced and non-enhanced tumors with non-enhanced tumors having higher de novo GMP synthesis.

[0327] The ratio of de novo GMP synthesis can be quantified using time-course U13C glucose tracing and the INST-MFA model. The INST-MFA results can be compared with the machine learning results. Fluxes can be estimated using sc-RNAseq data and flux balance analysis from patients, and these estimated results can be compared with machine learning predictions.

[0328] It should be understood that the foregoing detailed description and the appended examples are merely illustrative and should not be considered as limiting the scope of the present disclosure, which is defined only by the appended claims and their equivalents.

[0329] Various changes and modifications to the disclosed embodiments will be apparent to those skilled in the art. Such changes and modifications can be made without departing from the spirit and scope of the invention, including but not limited to those related to chemical structures, substituents, derivatives, intermediates, synthesis, compositions, formulations, or methods of use.

[0330] Any patents and publications cited herein are hereby incorporated by reference in their entirety.

Claims

1. A method for estimating the absolute metabolic flux of a metabolic pathway of interest, the method comprising: a) Administering a tracer to a subject; b) Collecting a sample from the subject; and c) Generating an estimate of the absolute metabolic flux of the pathway of interest.

2. The method according to claim 1, wherein The estimate of the absolute metabolic flux of the pathway of interest is generated based on the levels of one or more metabolites and / or their isotopologues in the sample at a single time point after administering the tracer to the subject.

3. The method according to claim 1 or claim 2, wherein, The pathway of interest is the purine synthesis pathway.

4. The method according to claim 3, wherein The one or more metabolites and / or their isotopologues include one or more of the following: ribose-5-phosphate (R5P), glycine (GLY), carbon dioxide (CO2), 5-methyltetrahydrofolate (C-THF), inosine monophosphate (IMP), inosine, hypoxanthine, guanine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine, adenosine monophosphate (AMP), and adenosine.

5. The method according to claim 3 or claim 4, further comprising determining the contribution ratio of de novo synthesis of GMP and / or de novo synthesis of IMP in the purine synthesis pathway.

6. The method according to claim 1 or claim 2, wherein The pathway of interest is the pyrimidine synthesis pathway.

7. The method according to claim 6, wherein, The one or more metabolites and / or their isotopologues include one or more of ribose-5-phosphate (R5P), aspartic acid (ASP), carbon dioxide (CO2), uridine, and uridine monophosphate (UMP).

8. The method according to claim 1 or claim 2, wherein, The pathway of interest is the serine synthesis pathway.

9. The method according to claim 8, wherein The one or more metabolites and / or their isotopologues include one or more of 3-phosphoglycerate (3PG), glycine (gly), and 5,10-methylenetetrahydrofolate (Me-THF).

10. The method according to any one of claims 1-9, wherein The sample is a tissue sample.

11. The method according to claim 10, wherein, The subject has cancer, and wherein the tissue sample includes a tumor tissue sample.

12. The method according to claim 1, wherein, The cancer is brain cancer.

13. The method according to claim 12, wherein The brain cancer is glioblastoma.

14. The method according to any one of claims 11 - 13, wherein, The estimate of the absolute metabolic flux of the pathway of interest is generated based on the levels of one or more metabolites and / or their isotopologues in the sample at a single time point after administering radiotherapy to the subject.

15. The method according to any one of claims 1-14, wherein, The estimate of the absolute metabolic flux of the pathway of interest is generated using an artificial intelligence / machine learning (AI / ML) model.

16. The method according to any one of claims 1-15, wherein, The tracer includes a part labeled with 13 C, 15 N, 18 O or 2 D.

17. The method according to claim 16, wherein The moiety includes glucose, methionine, serine, glutamine, lactate, acetate, hypoxanthine, or uridine.

18. A method for selecting a therapy for a subject in need thereof, the method comprising: a) Using the method according to any one of claims 1-17 to generate an estimate of the absolute metabolic flux of the pathway of interest, and b) Selecting a therapy for the subject in need thereof based on the estimate of the absolute metabolic flux of the pathway of interest.

19. The method according to claim 18, wherein, The subject has cancer, and wherein the pathway of interest is a cancer-related pathway.

20. The method according to claim 19, wherein The cancer is brain cancer.

21. The method according to claim 20, wherein, The brain cancer is glioblastoma.

22. The method according to any one of claims 18 - 21, wherein, The pathway of interest is the purine synthesis pathway.

23. The method according to any one of claims 18 - 21, wherein The pathway of interest is the pyrimidine synthesis pathway.

24. The method according to any one of claims 18 - 21, wherein, The pathway of interest is the serine synthesis pathway.

25. The method according to any one of claims 18 - 24 further comprises administering a selected therapy to the subject.

26. The method according to any one of claims 18 - 25, wherein, The therapy is inosine monophosphate dehydrogenase (IMPDH) inhibitor and / or dietary serine restriction.

27. A machine learning method for estimating the absolute activity of one or more metabolic fluxes, the method comprising: a) administering a tracer to a subject; b) obtaining a plurality of measurements from a sample collected from the subject, wherein each measurement is the level of a metabolite and / or its isotopologues in a metabolic pathway of interest at a single time point; and c) applying an artificial intelligence / machine learning (AI / ML) model to the measurements to generate an estimate of the absolute activity of one or more metabolic fluxes.

28. The method according to claim 27, wherein, The pathway of interest is the purine synthesis pathway.

29. The method according to claim 28, wherein, The one or more metabolites and / or their isotopologues comprise one or more of the following: ribose - 5 - phosphate (R5P), glycine (GLY), carbon dioxide (CO2), 5 - methyltetrahydrofolate (C - THF), inosine monophosphate (IMP), inosine, hypoxanthine, guanine, guanosine monophosphate (GMP), guanosine diphosphate (GDP), guanosine, adenosine monophosphate (AMP), and adenosine.

30. The method according to claim 28 or claim 29 further comprises determining the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway.

31. The method according to claim 27, wherein, The pathway of interest is the pyrimidine synthesis pathway.

32. The method according to claim 31, wherein, The one or more metabolites and / or their isotopologues comprise one or more of ribose - 5 - phosphate (R5P), aspartic acid (ASP), carbon dioxide (CO2), uridine, and uridine monophosphate (UMP).

33. The method according to claim 27, wherein The pathway of interest is the serine synthesis pathway.

34. The method according to claim 33, wherein The one or more metabolites and / or their isotopologues comprise one or more of 3 - phosphoglycerate (3PG), glycine (gly), and 5,10 - methylene - THF (Me - THF).

35. The method according to any one of claims 27 - 34, wherein The sample comprises a tissue sample.

36. The method according to claim 35, wherein, The subject is diagnosed with cancer or at risk of developing cancer.

37. The method according to claim 36, wherein, The cancer is brain cancer.

38. The method according to claim 37, wherein, The brain cancer is glioblastoma.

39. The method according to any one of claims 27 - 38, wherein The tissue sample is a tumor tissue sample.

40. The method according to any one of claims 27 - 39, wherein, The tracer includes a part labeled with 13 C, 15 N, 18 O or 2 D.

41. The method according to claim 40, wherein The moiety comprises glucose, methionine, serine, glutamine, lactate, acetate, hypoxanthine, or uridine.

42. The method according to any one of claims 36 - 41, wherein The plurality of measurements are obtained from a sample collected after administering radiotherapy to the subject.

43. A method for selecting a therapy for a subject in need thereof, the method comprising: a) estimating the absolute activity of one or more metabolic fluxes by the method according to any one of claims 27 - 42; and b) selecting a therapy for the subject in need thereof based on the estimated absolute activity of the one or more metabolic fluxes.

44. The method according to claim 43, wherein, The therapy is inosine monophosphate dehydrogenase (IMPDH) inhibitor and / or dietary serine restriction.

45. The method according to claim 43 or claim 44 further comprises the step of administering the selected therapy to the subject.

46. A method for selecting a therapy for a subject with cancer, the method comprising: a) Determining the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis in the purine synthesis pathway by the method according to claim 5 or claim 30; and b) Selecting an inosine monophosphate dehydrogenase (IMPDH) inhibitor for the subject when the contribution ratio of de novo GMP synthesis and / or de novo IMP synthesis is increased relative to a threshold.

47. The method according to claim 46, wherein, The subject has brain cancer.

48. The method according to claim 47, wherein, The brain cancer is glioblastoma.

49. A method for selecting a therapy for a subject with cancer, the method comprising: a) Determining the absolute activity of the serine synthesis pathway by the method according to claim 8, 9, 33 or 34; and b) Selecting dietary serine restriction for the subject when the absolute activity of the serine synthesis pathway is decreased relative to a threshold.

50. The method according to claim 49, wherein, The subject has brain cancer.

51. The method according to claim 50, wherein, The brain cancer is glioblastoma.

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