Decoding Mixture Perception through Computational Modeling of Component Interactions

I. INTRODUCTION

• Multi-molecule odors create a high-dimensional mapping shaped by molecule types, concentrations, inter-molecule interactions, and receptor activation integration.These factors make mixture decoding substantially more complex than single-molecule odor-perception mapping.Source: §I · p. 2, Figure 1 · p. 2
• Single-molecule odor-perception data guide mixture recognition by transferring knowledge from a semantically rich molecular space.This strategy addresses the lack of sufficient labeled mixture-perception data for end-to-end training.Source: §I · pp. 2–3
• 92.2% accuracy was achieved on a newly curated real-world dataset, demonstrating accurate mixture odor-perception identification.The experiments evaluated response-curve modeling, response–perception alignment, mixture similarity recognition, and mixture perception identification.Source: §I · p. 3
• The framework predicts molecule–receptor neural response curves and fuses receptor- and concentration-dependent responses to model mixture perception.Its workflow includes attention-weighted multi-receptor fusion and concentration-aware multi-molecule fusion.Source: §I · pp. 2–3, Figure 2 · p. 4

A. Robustness Validation of Neural Response Curves

• 0.925 curve similarity was achieved against real neural response curves from 35 biochemical mixture-response pairs.The validation set represented dynamic receptor responses induced by mixtures with substantially different concentration ratios.Source: A. Robustness Validation of Neural… · p. 5
• Curve similarities for RF, CNN, DKNN, GNN, POM, and MolFormer were 0.712, 0.732, 0.765, 0.802, 0.835, and 0.864, respectively.These values were all below the method’s 0.925 matching score.Source: A. Robustness Validation of Neural… · p. 5
• Our method’s predicted neural response curves showed the closest alignment with ground-truth curves among the compared models.Comparisons included RF, CNN, DKNN, GNN, POM, and MolFormer.Source: A. Robustness Validation of Neural… · p. 5, Figure 3 · p. 6
• Our method achieved the highest matching accuracy across the evaluated multi-molecule mixtures.Figure 3 compares predicted curves, matching accuracy, peak alignment, and per-mixture matching accuracy.Source: Figure 3 · p. 6

B. Performance of Discrepancy Alignment Between Response Curves and Odor Perceptions

• The evaluation used pairwise comparisons across a dataset of 5,023 molecules to assess the response–perception relationship.Representative molecules were selected to cover functional-group, chemical-category, and structural diversity.Source: B. Performance of Discrepancy… · p. 7
• r = 0.921 was obtained between odor-perception differences and predicted neural response-curve differences.The result indicates that larger perceptual differences generally corresponded to larger response-curve discrepancies.Source: B. Performance of Discrepancy… · p. 7
• The method’s correlation exceeded RF (0.521), CNN (0.558), DKNN (0.635), GNN (0.721), POM (0.815), and MolFormer (0.821).The comparison evaluated how well each method captured the relationship between curves and perceptual similarity.Source: B. Performance of Discrepancy… · p. 7
• Correlation remained consistently high for molecules associated with 1 to 15 odor perceptions.Other models’ average performance gradually declined as the number of associated odor perceptions increased.Source: B. Performance of Discrepancy… · pp. 7–8

C. Evaluation of Odor Perception Similarity for Mixtures

• The real evaluation dataset contained 112 mixtures with component annotations and human-sensory ground-truth similarity scores.These annotations supported direct comparison between predicted and observed mixture perceptual similarity.Source: C. Evaluation of Odor Perception… · p. 9
• r = 0.931 correlation and 0.072 MAE were achieved for mixture perceptual similarity against human sensory ground truth.Amit et al. and Ravia et al. obtained correlations of 0.811 and 0.834, with MAEs of 0.352 and 0.224.Source: C. Evaluation of Odor Perception… · p. 9, Figure 5 · p. 10
• Against POM and MolFormer, the method achieved higher correlations of 0.931 versus 0.721 and 0.755, and lower MAEs of 0.072 versus 0.415 and 0.381.These advanced molecular models first predicted molecule perceptions and then combined them using concentration weighting.Source: C. Evaluation of Odor Perception… · p. 9, Figure 5 · p. 10
• The method achieved 0.942 matching accuracy for the 16 most frequent odor perceptions, exceeding Ravia et al. (0.836), Amit et al. (0.795), MolFormer (0.772), and POM (0.715).Its predicted perceptual distribution aligned most closely with the ground-truth distribution.Source: C. Evaluation of Odor Perception… · pp. 9–10

D. Evaluation of Odor Perception Recognition for Mixtures

• The evaluation used 172 challenging mixtures with diverse chemical compositions, precise concentration ratios, and odor perceptions for raw materials and natural mixtures.Baseline models first predicted individual-molecule odors and then derived mixture perception from those predictions.Source: D. Evaluation of Odor Perception… · pp. 10–11
• 0.942 cosine similarity was obtained against human ground-truth odor perceptions, exceeding RF, CNN, DKNN, GNN, POM, and MolFormer.The compared models achieved 0.657, 0.661, 0.742, 0.774, 0.814, and 0.832, respectively.Source: D. Evaluation of Odor Perception… · p. 11
• 0.922 ± 0.016 accuracy, with AUROC of 0.924 ± 0.031 and AUPRC of 0.919 ± 0.018, was achieved on mixture odor-perception prediction.Precision, recall, and specificity were 0.932 ± 0.028, 0.916 ± 0.052, and 0.915 ± 0.021, respectively.Source: D. Evaluation of Odor Perception… · p. 11
• All evaluated common odor perceptions achieved recognition accuracies above 0.9 despite substantial molecule sharing among frequent odors.The analysis ranked recognition accuracy at the odor-category level across mixtures.Source: D. Evaluation of Odor Perception… · p. 12

Ⅰ. Materials and Datasets

• Single-molecule receptor and perception datasets were collected for training, while real-world mixture data were gathered for evaluation.The mixture resources included similarity ratings between mixture pairs and compositions with corresponding odor perceptions.Source: Ⅰ. Materials and Datasets · pp. 15–16
• The molecule–receptor and molecule–odor datasets have imbalanced feature distributions across receptors, molecules, and odor labels.The supplementary description reports skewed associations and uneven numbers of odor descriptors per molecule.Source: Figure S1 · p. 15

A. Molecule-Receptor Dataset

• The dataset contains single molecules paired with the olfactory receptors to which they respond.Its feature distribution is presented in Figure S1a.Source: A. Molecule-Receptor Dataset · p. 16
• Molecule–receptor relationships were compiled from ODORDB, ODORactor, OlfactionDB, and other studies containing receptor interaction information.These sources were described as widely used resources validated through real-world studies.Source: A. Molecule-Receptor Dataset · p. 16
• 5,023 distinct single molecules were linked with 104 olfactory receptors in the curated dataset.The dataset was used for subsequent biologically grounded modeling of mixture olfactory perception.Source: A. Molecule-Receptor Dataset · p. 16

B. Molecule-Perception Dataset

• Single-molecule perception correspondences were curated to guide mixture odor prediction and optimize the model.The dataset was assembled because large-scale mixture–odor correspondence data are scarce.Source: B. Molecule-Perception Dataset · p. 16
• Good Scents and Leffingwell provide molecules labeled with one or more odor descriptors based on expert empirical testing.Both databases were described as publicly available and validated through biochemical experiments.Source: B. Molecule-Perception Dataset · p. 16
• Duplicate, missing, erroneous, and inconsistent records were removed to improve dataset consistency and reduce noise and bias.Cross-dataset validation was used to retain consistent and reliable data points.Source: B. Molecule-Perception Dataset · p. 17

• 524 unique molecules form 112 mixtures with 381 pairwise similarity comparisons.Source: C. Mixture Similarity Rating Dataset · p. 17
• Mixture complexity ranges from 4 to 43 constituent molecules, covering combinations from a few components to several dozen.Source: C. Mixture Similarity Rating Dataset · p. 17
• Each trial presents subjects with two mixture stimuli for perceptual similarity rating.Source: C. Mixture Similarity Rating Dataset · p. 17

• The validation dataset combines composition data from Essential Oil Safety with odor labels from the Good Scents Company database.Source: D. Mixture–Perception Dataset · p. 17
• Natural mixtures are represented by constituent molecules and their corresponding concentration ratios.Source: D. Mixture–Perception Dataset · p. 17
• 172 real-world test samples provide an independent benchmark for evaluating mixture odor-perception recognition.Source: D. Mixture–Perception Dataset · p. 18

• 35 experimentally measured mixture–response curve pairs were curated from 22 published olfactory-receptor studies.Source: E. Mixture-Response Curve Dataset · p. 18
• The framework integrates molecule–receptor modeling, receptor fusion, concentration-aware mixture fusion, and response-curve similarity to connect chemical mixtures with perception.Source: Ⅱ. Overall Workflow of Multi-Molecule… · pp. 18–20

Step 1 (Figure 2a)

• The model predicts molecule–receptor response curves from molecular sequence features and three-dimensional receptor structure using DNDF and HGNN representations.Source: Ⅱ. Overall Workflow of Multi-Molecule… · p. 19

Step 2 (Figure 2b)

• Response-curve discrepancies are aligned with odor-perception differences so single-molecule data can guide mixture-perception recognition.Source: Ⅱ. Overall Workflow of Multi-Molecule… · p. 19

Steps 3–4 (Figures 2c–2d)

• Attention-weighted fusion assigns unequal receptor contributions, while concentration-aware fusion captures concentration effects on mixture response profiles.Source: Ⅱ. Overall Workflow of Multi-Molecule… · pp. 19–20

Step 5 (Figure 2e)

• Mixture odor perception is determined by comparing mixture response curves with single-molecule curves and weighting corresponding odor-perception vectors.Source: Ⅱ. Overall Workflow of Multi-Molecule… · p. 20

Data Features of Molecule and Receptor

• A fully connected network predicts molecule–receptor neural response curves using a decaying sine wave to simulate adaptation and receptor desensitization.The curve uses exponential damping for decay toward baseline and a periodic term for dynamic response characteristics.Source: (3) Single-Molecule to Single-Receptor… · pp. 21–22, Figure S2 · p. 22
• Perception-guided unsupervised training aligns neural-response discrepancies with odor-perception differences when real neural response recordings are scarce.The objective is to make differences between response-curve patterns isomorphic to perceptual odor differences.Source: B. Align Discrepancy Between Response… · pp. 22–23, Figure S3 · p. 23
• Concentration-aware molecule fusion and attention-weighted receptor fusion produce a global neural response curve for each multi-molecule mixture.Molecule contributions are combined according to mixture concentration, while receptor contributions are dynamically weighted before integration.Source: Ⅲ. Formulation Implementation · p. 26, (2) Integration Across the Olfactory… · p. 32
• DNDF models molecular structural features, while HGNN represents receptor atoms as nodes and chemical bonds as hyperedges to capture 3D topology.DNDF combines differentiable decision trees with neural representation learning; HGNN encodes spatial dependencies relevant to ligand binding.Source: (2) Deep Learning Modeling for… · p. 21, (2) Feature Extraction and Modeling · p. 27
• Attention-based feature extraction replaces DNDF’s original CNN module to handle sparse, high-dimensional molecular sequence inputs.The replacement combines multi-head self-attention with a fully connected network to extract informative molecular feature vectors.Source: (2) Feature Extraction and Modeling · p. 27, A. Improvements to DNDF · p. 33

B. Improvements to HGNN

• Hierarchical multi-scale hypergraphs represent receptor structure across atomic, residue, and higher structural levels while incorporating biological interaction constraints.The atomic level models interactions such as chemical bonds, hydrogen bonds, and hydrophobic interactions; higher levels capture broader receptor organization.Source: B. Improvements to HGNN · p. 34
• Transformer-based receptor feature augmentation uses amino acid sequences to capture global sequence features, cross-sequence synergistic effects, and functional–structural correlations.The resulting representations are described as more discriminative and biologically interpretable for downstream tasks.Source: B. Improvements to HGNN · pp. 34–35
• Adaptive cross-modal attention aligns receptor sequence semantics with three-dimensional structural features through bidirectional interactions instead of simple feature concatenation.Sequence features attend to structural features and structural features attend to sequence features, addressing multimodal heterogeneity.Source: B. Improvements to HGNN · p. 35
• The enhanced fully connected module fuses molecule and receptor features using bidirectional cross-modal attention to identify binding-relevant atomic and residue patterns.Attention can focus on receptor binding regions and molecular functional groups, providing a structurally interpretable basis for response-curve predictions.Source: C. Enhanced Fully Connected Network… · pp. 35–36
• Residual connections and gated multi-scale fusion are added to improve feature-extraction depth and training stability.Skip connections in residual blocks are intended to mitigate vanishing gradients during deep-network training.Source: C. Enhanced Fully Connected Network… · p. 36

A. Model Training

• The dataset is split into training, validation, and independent test sets in an 8:1:1 ratio, with the test set reserved for final reporting.Ten-fold cross-validation is additionally used during training, and reported results are averaged across folds.Source: A. Model Training · pp. 36–37
• POM and MolFormer provide strong single-molecule perception baselines but do not explicitly model three-dimensional interactions, biological transduction, or concentration-dependent mixture effects.POM lacks explicit competitive or synergistic multi-molecule interaction modeling, while MolFormer uses sequence-based SMILES representations without explicit 3D interaction structure.Source: B. Advanced Models · pp. 37–38

Applications

• The framework is proposed for embodied robotic perception in safety monitoring, healthcare, and environmental interaction scenarios.Its stated role is to provide robots with interpretable olfactory perception capabilities.Source: (1) Embodied Intelligent Robots · p. 38
• The method is proposed as a computer-aided tool for flavor and fragrance formulation under different molecule combinations and concentration ratios.The stated motivation is to reduce reliance on costly, time-consuming expert trial and error.Source: (2) Food and Flavor Industry · p. 38
• The framework is also proposed for complex-odor environmental monitoring, electronic noses, and digital olfaction or virtual-reality interaction.These applications target mixtures that are difficult to assess with single-sensor or limited-primitive approaches.Source: (3) Environmental Monitoring · p. 39, (4) Digital Olfaction · p. 39

Limitations and Future Work

• The model’s internal decision-making remains opaque, and its current predictions do not account for individual differences in odor perception.The paper identifies attention-based explainability and integration of genomic and demographic information as future directions.Source: (1) Enhancement of Model Explainability · p. 39, (2) Expansion of Personalized Perception · pp. 39–40