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Thermodynamic Quality Control Reshapes Spatially Resolved Metabolic Flux Predictions in Prostate Cancer

Mohammad Reza ZargariD, Sunayana Malla, Rajib SahaiD, Ratul ChowdhuryiD

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Abstract

Spatial transcriptomics enables region-resolved investigation of tumor metabolism, yet translating gene expression into reliable metabolic flux predictions remains challenging because genome-scale models can admit thermodynamically infeasible cycles (TICs). Here, we integrated spatial transcriptomic data from twelve annotated regions of a single prostate tumor, spanning normal, inflamed, and Gleason 3+3 and 3+4 tissues, with Human-GEM using an E-Flux framework incorporating defined nutrient constraints, explicit cycle certification, and loopless flux variability analysis. An initial naive implementation produced TICs in all twelve flux solutions, with total internal fluxes 190-890-fold higher than those obtained using the revised workflow. All flux solutions were certified free of TICs, and 94.7% of 17,592 loopless flux bounds were determined exactly. Within the analyzed tissue, predicted metabolic similarity was associated with spatial region (permutation p = 0.023) but not histological state (p = 0.52), revealing model-predicted heterogeneity even between regions sharing the same Gleason grade. Flux-based target prioritization identified fatty acid uptake-associated genes (CD36, FABPs, and SLC27A1/4), although the dominant uptake signal was confined to one malignant region, suggesting a localized metabolic hypothesis rather than an established therapeutic vulnerability. Analysis of the zinc-citrate-aconitase axis further demonstrated that zinc-dependent citrate redistribution was absent under baseline conditions and emerged only when oxidative demand, elimination of a cytosolic aconitase bypass, and strong mitochondrial aconitase inhibition coincided. These findings establish the importance of thermodynamic quality control and physiologically informed constraints in spatial metabolic modeling, while distinguishing computationally feasible flux predictions from experimentally validated metabolic mechanisms. The resulting framework provides a reproducible foundation for investigating spatial metabolic heterogeneity and prioritizing testable hypotheses for future experimental validation.

In-depth summary

Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 2 (21 Oct 2026) · CC BY 4.0

Quality-controlled, cycle-certified E-Flux Human-GEM models of twelve regions from one prostate tumor curb implementation-driven flux inflation and show predicted metabolic similarity tracks spatial region, not histology.

Converting spatial transcriptomes into genome-scale metabolic fluxes is vulnerable to thermodynamically infeasible cycles, open nutrient exchanges and solver-dependent solutions, and a prior mCADRE-pruned prostate study neither compared flux magnitudes across regions nor reported cycle checks. This work quantifies how implementation choices alter fluxes and target rankings, and provides a certified loop-free E-Flux workflow with exactness-labeled loopless flux ranges.

Key results

  1. ShownA conventional E-Flux setup produced infeasible cycles (TICs) at every position and inflated internal fluxes through several implementation choices, not cycles alone; open exchanges let the network import lactate, citrate and pyruvate to fuel most growth, and cycle presence depended on the solver.

    Initial loop certificate 74–125 at all twelve positions; cycles carried 1.2–6.8% of internal flux; internal totals 48,722–66,322 a.u. vs 57–310 a.u. after revision (190- to 890-fold). Limiting uptake to the defined medium cut mean biomass from 2.92 to 0.025 a.u.; a HiGHS re-solve gave totals of 436–511,678 a.u. with a cycle in one position. · Abstract; 3.1 Modeling assumptions and infeasible cycles…

  2. ShownThe revised workflow (defined medium, pFBA, CycleFreeFlux) returned certified cycle-free solutions at every position, a completeness-checked catalogue of TIC-capable reactions, and exactness-annotated loopless flux bounds that, for TIC-participating reactions, were often far narrower than standard ranges.

    2,273 of 11,274 internal Human-GEM reactions (20.2%), mostly transporters, can join a TIC. Of 17,592 loopless bounds (733 reactions in 12 positions), 94.7% were exact and 5.3% conservative (4.3–7.8% per position); the loop law removed 4.0–20.1% of total standard FVA span per position. · 2.3 Certified loop-free flux solutions and flux…; 3.1 Modeling assumptions and infeasible cycles…

  3. SuggestedWithin this single tumor, predicted flux profiles grouped by spatial region rather than histological state, and same-diagnosis positions could diverge: the two Gleason 3+3 positions differed more than an average pair, while inflamed positions from separate regions were nearly identical.

    Correlation distance within vs between regions 0.029 vs 0.037 (position-level permutation p = 0.023, 10,000 permutations); same vs different state 0.038 vs 0.034 (p = 0.52). Gleason 3+3 pair distance 0.059 vs mean of all pairs 0.035; inflamed pair 0.003. Biomass did not differ by state (Kruskal–Wallis p = 0.73). · 2.4 Spatial heterogeneity; 3.2 Predicted metabolic similarity is associated…; 3.3 Exploratory within-grade comparisons reveal…

  4. SuggestedFlux-based scoring prioritized one long-chain fatty-acid uptake reaction shared by CD36, FABPs and SLC27A1/4, carrying flux only in Gleason 3+3 position P1.2; de novo lipogenesis (FASN, ACLY) carried no flux, and TCGA-PRAD and DepMap data offered little concordant support.

    Thirteen genes (four reactions) passed criteria; top reaction MAR00155 (score 14.96) had non-zero flux only in P1.2 (2.07 a.u.). Ranking vs standard FVA or no ΔFVA term: ρ 1.00 and 0.9998; additive rank-sum ρ = 0.67 (15/20 shared). Lipid removal cut biomass 8–17%. CD36 TCGA log2FC −1.40; CD36 essential only in 22Rv1 (Chronos −0.51). · 2.6 Target scoring and lipid dependence; 3.4 Flux-based prioritization identifies a…; 3.5 Independent datasets highlight the limits of…

  5. SuggestedBaseline models showed no zinc effect on citrate fate; in post hoc stress tests, zinc-sensitive citrate secretion emerged only when oxidative demand, a blocked cytosolic aconitase (ACO1) bypass and near-complete mitochondrial aconitase inhibition coincided, without changing growth.

    Pre-specified test: ACO2 and citrate synthase flux zero in all 216 simulations; biomass shifted < 10⁻¹⁰ between zinc levels. Post hoc, carbon-uptake caps raised ATP-synthase share from 1.1–12.3% to 22–94%; with ACO1 route blocked, θ* spanned 20 to 17,608 (median 398), and normal-like zinc raised citrate secretion in 5 of 12 positions only at ≥97–99% inhibition. · 2.7 Energy metabolism and the zinc-citrate axis; 3.7 Baseline expression-constrained models do…; 3.8 Constraint-based stress testing identifies…

Methods, data and reproducibility

Region-averaged spatial transcriptomes set E-Flux reaction bounds on Human-GEM (GPR AND = min, OR = sum) under a defined RPMI-1640 plus serum medium; parsimonious FBA and CycleFreeFlux solutions were certified loop-free by a linear program, with loopless flux variability analysis at ≥95% biomass, flux-based target scoring and zinc-aconitase simulations.

  • Berglund et al. prostate cancer spatial transcriptomics; region-averaged expression for annotated positions P1.1–P4.3 in four regions (100 µm spots) · human · n = twelve positions, one patient (6 normal, 2 inflamed, 4 cancer) · CNGB STOmics STDS0000053
  • Human-GEM genome-scale metabolic model with an added 60-component prostate biomass reaction and a defined medium of RPMI-1640 plus lipid, cholesterol and trace-element components of 10% FBS · human · n = 12,934 reactions (12,931 before additions)
  • TCGA-PRAD bulk RNA-seq expression (GDC STAR-TPM) used for tumor vs normal comparison of prioritized and reference genes · human · n = 497 primary tumors, 51 solid-tissue normals · TCGA-PRAD
  • DepMap 24Q4 CRISPR Chronos gene effects for prostate adenocarcinoma lines (PC-3, VCaP, 22Rv1, LNCaP, DU145) and non-cancerous prostate lines · human (cell lines) · n = 5 cancer lines, 5 non-cancerous lines
  • Illustrative crystal structures: BbZIP, a ZIP-family homologue of ZIP1, and mitochondrial aconitase bound to citrate · Bordetella bronchiseptica; bovine · PDB 5TSA; PDB 1C96
Methods & tools
Human-GEM, COBRApy v0.29.1, HiGHS solver, E-Flux, parsimonious FBA (pFBA), CycleFreeFlux, Loop certificate linear program (cycle certification), Loopless flux variability analysis with cycle-cut MILP, SciPy v1.11, DESeq2 v1.42, Position-level permutation test (Mann–Whitney U statistic), DepMap Chronos gene effects
Software & environment
Python 3.11 with COBRApy v0.29.1, SciPy v1.11 and DESeq2 v1.42; linear programs solved with HiGHS; full package versions reportedly documented in the not-yet-released repository README.
Reproducibility gaps
The study's own code repository URL is pending until acceptance, and the Supporting Information (supplementary tables, methods and notes defining the medium, biomass and algorithms) has no link yet.
Limitations (6)
  • Data derive from a single patient, so the twelve positions are not independent biological replicates and could share section-level technical artifacts; no new experiments were run, and TCGA-PRAD and DepMap measure transcript abundance and essentiality rather than flux. · stated by the authors
  • Averaging expression over each annotated region mixes epithelial, stromal and immune signals; deconvolving cell types or modeling individual spots on finer-resolution platforms might alter the predictions. · stated by the authors
  • Predicted fluxes are uncalibrated relative capacities (a.u.) tied to an assumed biomass objective and culture-like medium; kinetics, post-translational control and metal-dependent inhibition are not modeled, and the ATP-synthase share reflects how E-Flux bounds multi-subunit complexes. · stated by the authors
  • Target rankings shift with the scoring formula and hinge on a single position; the zinc-condition simulations were designed post hoc and use aconitase capacities inferred from citrate synthase expression plus assumed nutrient caps; 5.3% of loopless bounds are conservative. · stated by the authors
  • Human-GEM gene coverage ranged from 28.7% to 67.0% across positions, and undetected genes were set to each position's minimum positive expression; inter-position flux distances may partly track detection depth, which was not tested. · noted in this summary
  • Similarity and clustering analyses use one parsimonious point solution per position rather than sampling the loop-free solution space, so region associations could depend on which alternative optimum is returned. · noted in this summary

Read this if you build expression-constrained genome-scale metabolic models from spatial transcriptomes and want a concrete checklist for certifying loop-free fluxes and auditing nutrient and reaction-bound assumptions.

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