Additional file 2 of Multimodal learning reveals plants’ hidden sensory integration logic

Supplementary Material 2: Table S1. Gene markers used for correlation analysis with UMAP axes. Figure S1. Functional annotation of effector-associated biological processes and protein domains. Enriched terms highlight iron/manganese ion homeostasis (e.g., transmembrane transport, vacuolar sequestration) mediated by VIT family transporters, alongside ATP-dependent RNA helicase activity (DEAD/DEAH box domains). Terms are clustered by functional similarity, reflecting coordinated roles in metal trafficking and RNA metabolism during effector activity. Figure S2. Unimodal data separability and model calibration analysis. (A, B, C) Calibration curve and confidence distribution demonstrate the model’s well-calibrated predictions, with 50% of cases falling in the high-confidence range ( $$0.75-0.92$$ ) and no evidence of overconfidence. (D) Principal component analysis (PCA) of transcriptomic data shows clear separation of effector groups (GLOIN781 vs. GLOIN707) along PC1 (78.3% variance explained). (E, F) Phenomic and metabolomic profiles exhibit partial overlap between effectors (RiSP749, GLOIN781, OPF, GLOIN707), highlighting the need for multimodal integration. Figure S3. Extended analysis of phenotypic regression and embedding interpretability. (A-B) Trait-specific $$R^2$$ (MSE) scores from phenotypic regression, highlighting stronger predictability for architectural traits. Corresponding mean squared errors reveal higher uncertainty in physiological traits such as anthocyanin accumulation. Performance was evaluated by training a ridge regression model on the learned latent CoMM embeddings Z as features to predict each phenotypic trait.(C) Top 20 most important embedding dimensions for genotype classification using random forest feature importance. (D) SHAP-based interpretability of embeddings per effector class (GLOIN707, GLOIN781, RiSP749, GFP), showing feature-level specificity across dimensions. Figure S4. Cross-modal attention analysis between transcriptomic and metabolomic modalities. (A) Scatter plot comparing prior weights ( $$P_{ij}$$ ) against learned attention weights ( $$A_{ij}$$ ) for RNA-metabolite interactions, coloured by the delta value ( $$\Delta = A_{ij} - P_{ij}$$ ). Points along the identity line (dashed) indicate interactions where the model maintained prior biological knowledge, while deviations represent novel discoveries or suppressed relationships. (B) Top 15 novel RNA-metabolite discoveries ranked by delta values, showing gene-metabolite pairs where the model learned stronger associations than the baseline prior. Gene identifiers (e.g., Solyc10g000881) are paired with metabolite names, revealing potential novel biological relationships. (C) Distribution of delta values across all RNA-metabolite interactions, showing the frequency of different magnitudes of deviation from prior expectations. The vertical dashed line at $$\Delta = 0$$ indicates no change from prior. (D) Heatmap visualisation of the delta matrix for the first 50 RNA features against all 18 metabolite features, showing spatial patterns of enhanced (positive $$\Delta$$ , red) and suppressed (negative $$\Delta$$ , blue) cross-modal interactions. The analysis reveals both global patterns and specific feature-level modifications of biological priors through multimodal integration. Figure S5. Detailed Cross-Modal Integration Hub. This schematic represents an integrative analysis framework connecting three primary data modalities: (1) Metabolite profiles capturing biochemical states, (2) Gene expression patterns, and (3) Trait measurements including fractal dimension analysis, primary root length, and root swelling phenotypes. The hub facilitates the identification of multi-scale relationships between molecular components and macroscopic root architecture features, enabling comprehensive systems biology approaches to understand root development and adaptation.