IGM: Integrated Gene-expression Modeling for multi-condition flux-preserving genome-scale metabolic models.

Genome-scale metabolic models (GEMs) are powerful tools for studying cellular metabolism, but conventional approaches such as Flux Balance Analysis (FBA) often yield ambiguous results due to the lack of consistent integration of condition-specific data across multiple experimental contexts. Existing methods for incorporating gene expression data into GEMs are typically limited to single-condition analyses, rely on arbitrary thresholds, or compromise the interpretability of flux predictions. Here, we present IGM: Integrated Gene-expression Modeling, a novel mixed-integer linear programming (MILP) framework that integrates gene expression data across multiple conditions into GEMs without binarization, thereby preserving flux units and enhancing biological relevance. IGM employs flux variability analysis (FVA) to define feasible flux ranges, integrates relative gene expression through gene-protein-reaction (GPR) rules, and minimizes the difference between fluxes and corresponding gene expression mappings. Evaluation on Escherichia coli (E. coli) metabolic models demonstrates that IGM significantly improves correlation with experimentally measured fluxes, reduces flux solution ambiguity, and provides higher predictive consistency across multiple conditions. Among its variants, IGM with L1 norm regularization achieves the highest accuracy. We also evaluated gene expression integration by comparing relative gene expression values with model-derived gene expression variables. Visual inspection and genome-scale correlation analysis revealed strong concordance across all genes, confirming that IGM effectively preserves transcriptomic patterns while filtering out genes irrelevant to flux-carrying reactions, thereby enhancing biological interpretability. Furthermore, we applied IGM to flux change analysis, where subsystem-level fluxes revealed distinct metabolic states. This analysis highlights IGM's ability to integrate transcriptomic data into metabolic modeling in a condition-specific yet consistent manner, enabling biologically grounded predictions of metabolic adaptation. By capturing dynamic metabolic changes and improving predictive accuracy, IGM provides a robust framework for consistent, comparative, and multi-condition metabolic studies.