# Supplementary Materials

**Multi-Target Gene Therapy for Osteoarthritis: Dual-Axis Modeling and In Silico Validation**

**Author:** Po-Sung (Sinclair) Huang

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## Supplementary Tables

### Supplementary Table S1: Molecular Docking Results for ADAMTS-5

| Pose | Binding Affinity (kcal/mol) | RMSD l.b. (Å) | RMSD u.b. (Å) | Key Interactions |
|------|---------------------------|---------------|---------------|------------------|
| 1 | -4.795 | 0.000 | 0.000 | Zn coordination, H-bond His349 |
| 2 | -4.612 | 2.341 | 3.127 | Zn coordination, hydrophobic S1' |
| 3 | -4.523 | 1.876 | 2.654 | H-bond Glu346, hydrophobic |
| 4 | -4.418 | 3.012 | 4.231 | Partial Zn coordination |
| 5 | -4.287 | 2.567 | 3.891 | H-bond backbone |
| 6 | -4.156 | 3.456 | 4.782 | Hydrophobic only |
| 7 | -4.023 | 4.123 | 5.234 | Peripheral binding |
| 8 | -3.891 | 4.567 | 5.678 | Peripheral binding |
| 9 | -3.756 | 5.012 | 6.123 | Peripheral binding |

**Docking Parameters:**
- Software: AutoDock Vina 1.2.5
- Receptor: ADAMTS-5 catalytic domain (PDB: 3HY7)
- Ligand: Compound 097 (hydroxamate-based inhibitor)
- Grid box: 25 × 25 × 25 Å
- Grid center: Catalytic zinc
- Exhaustiveness: 32

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## Supplementary Table S2: Complete shRNA Design Parameters

### ADAMTS-5 Candidates

| ID | Position | Sequence (19-mer) | GC% | Reynolds | Tm (°C) | Off-targets | Selected |
|----|----------|-------------------|-----|----------|---------|-------------|----------|
| shADAMTS5-1 | 892-910 | GCAACTATGACGTGTTCAA | 42.1 | 9/9 | 54.2 | 0 | ✓ |
| shADAMTS5-2 | 1456-1474 | GGACATCTGTGCACATAAA | 42.1 | 8/9 | 52.8 | 0 | ✓ |
| shADAMTS5-3 | 2103-2121 | GCAGTATGAACTGGATGAA | 42.1 | 8/9 | 53.1 | 1 | ✓ |
| shADAMTS5-4 | 567-585 | GCTGATCAACGATGTCAAA | 42.1 | 7/9 | 52.4 | 0 | — |
| shADAMTS5-5 | 1892-1910 | GGAACTGTACTTGCATAAA | 36.8 | 7/9 | 51.2 | 2 | — |

### MMP-13 Candidates

| ID | Position | Sequence (19-mer) | GC% | Reynolds | Tm (°C) | Off-targets | Selected |
|----|----------|-------------------|-----|----------|---------|-------------|----------|
| shMMP13-1 | 678-696 | GCATCTGGAGTAACTGTAA | 42.1 | 9/9 | 53.6 | 0 | ✓ |
| shMMP13-2 | 1234-1252 | GGAGCATACTTGATTATAA | 36.8 | 8/9 | 50.8 | 0 | ✓ |
| shMMP13-3 | 456-474 | GCTAACGATGTCAACTGAA | 42.1 | 7/9 | 52.1 | 1 | — |
| shMMP13-4 | 987-1005 | GGCTGATACAGTCAATAAA | 36.8 | 6/9 | 49.4 | 0 | — |

**Reynolds Scoring Criteria (max 9 points):**
1. GC content 30-52%
2. No G/C at position 19
3. A/U at positions 15-19
4. A at position 3
5. U at position 10
6. G/C at position 1
7. Minimal internal repeats
8. Low thermodynamic stability at 5' end
9. No immunostimulatory motifs (5'-UGUGU-3', 5'-GUCCUUCAA-3')

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## Supplementary Table S3: Human-Canine Sequence Homology

| Protein | Human Accession | Canine Accession | Length (aa) | Identity (%) | Similarity (%) | Gaps (%) |
|---------|----------------|------------------|-------------|--------------|----------------|----------|
| SOX9 | NP_000337.1 | XP_038523857.1 | 509 | 98.2 | 99.0 | 0.0 |
| IL-1Ra | NP_776213.1 | XP_532370.2 | 177 | 77.4 | 86.4 | 1.1 |
| ADAMTS-5 | NP_009029.3 | XP_038284644.1 | 930 | 93.5 | 96.2 | 0.3 |
| MMP-13 | NP_002418.1 | XP_038284831.1 | 471 | 89.2 | 93.6 | 0.2 |
| IGF-1 | NP_000609.1 | NP_001003152.1 | 153 | 94.4 | 97.4 | 0.0 |

### Functional Domain Conservation

| Protein | Domain | Human Residues | Identity (%) | Key Motifs |
|---------|--------|----------------|--------------|------------|
| SOX9 | HMG box | 104-182 | 100.0 | DNA binding: RPMNAFMVW |
| SOX9 | Transactivation | 339-379 | 97.5 | PQ-rich |
| IL-1Ra | β-trefoil core | 25-152 | 88.3 | Receptor binding |
| IL-1Ra | Receptor interface | 12-23, 32-54 | 85.0 | Contact residues |
| ADAMTS-5 | Catalytic domain | 260-500 | 96.0 | HEXXHXXGXXH |
| ADAMTS-5 | Spacer (exosite) | 732-874 | 91.2 | Substrate positioning |
| MMP-13 | Catalytic domain | 100-260 | 92.0 | HEXXHXXGXXH |
| MMP-13 | Hemopexin | 271-471 | 87.5 | Substrate specificity |
| IGF-1 | Mature peptide | 49-118 | 100.0 | Receptor binding |
| IGF-1 | E-peptide | 119-153 | 85.7 | Processing signal |

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## Supplementary Table S4: Network Perturbation Raw Data Summary

### ECM Recovery Score Distribution

| Intervention | n | Mean | SD | Median | Min | Max | 95% CI Lower | 95% CI Upper |
|--------------|---|------|-----|--------|-----|-----|--------------|--------------|
| Control | 1000 | 43.6 | 12.1 | 43.2 | 12.4 | 78.9 | 42.8 | 44.4 |
| IL-1Ra only | 1000 | 52.3 | 10.8 | 52.1 | 22.7 | 81.3 | 51.6 | 53.0 |
| SOX9 only | 1000 | 58.7 | 9.4 | 58.5 | 31.2 | 84.6 | 58.1 | 59.3 |
| Multi-target | 1000 | 76.2 | 8.3 | 76.4 | 48.1 | 97.2 | 75.7 | 76.7 |

### Statistical Comparisons

| Comparison | Mean Difference | SE | t-statistic | p-value | Cohen's d |
|------------|-----------------|-----|-------------|---------|-----------|
| Multi vs Control | 32.6 | 0.46 | 70.87 | <0.001 | 3.16 |
| Multi vs IL-1Ra | 23.9 | 0.43 | 55.58 | <0.001 | 2.49 |
| Multi vs SOX9 | 17.5 | 0.40 | 43.75 | <0.001 | 1.97 |
| IL-1Ra vs Control | 8.7 | 0.51 | 17.06 | <0.001 | 0.76 |
| SOX9 vs Control | 15.1 | 0.49 | 30.82 | <0.001 | 1.39 |

### Synergy Calculation

| Metric | Value |
|--------|-------|
| Observed Multi-target Effect | 76.2 |
| Expected Additive (IL-1Ra + SOX9 - Control) | 67.4 |
| Synergy (Observed - Expected) | +8.8 |
| Synergy Index (Observed / Expected) | 1.13 |
| p-value (synergy > 0) | <0.001 |

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## Supplementary Methods S1: Network Perturbation Model Parameters

### Model Structure

The OA molecular network was modeled as a system of coupled ordinary differential equations (ODEs) with stochastic perturbation. The network comprised 16 nodes representing key molecular species:

**Axis I (Inflammatory):** IL-1β, TNF-α, NF-κB, COX-2, iNOS, PGE2, NO

**Axis II (Structural):** MMP-1, MMP-3, MMP-13, ADAMTS-4, ADAMTS-5, Collagen II, Aggrecan, SOX9

### Kinetic Parameters

| Parameter | Description | Value | Unit | Source |
|-----------|-------------|-------|------|--------|
| k_IL1_syn | IL-1β synthesis rate | 0.1 | h⁻¹ | Literature |
| k_IL1_deg | IL-1β degradation rate | 0.05 | h⁻¹ | Literature |
| K_NF_act | NF-κB activation constant | 10 | nM | Fitted |
| k_MMP_syn | MMP synthesis rate | 0.08 | h⁻¹ | Literature |
| k_COL_syn | Collagen synthesis rate | 0.02 | h⁻¹ | Literature |
| k_COL_deg | Collagen degradation rate | 0.01 | h⁻¹ | Literature |
| k_AGN_syn | Aggrecan synthesis rate | 0.03 | h⁻¹ | Literature |
| k_AGN_deg | Aggrecan degradation rate | 0.015 | h⁻¹ | Literature |

### Intervention Modeling

| Intervention | Target | Effect |
|--------------|--------|--------|
| IL-1Ra | IL-1β signaling | 80% inhibition |
| SOX9 overexpression | SOX9 activity | 3× baseline |
| IGF-1 | Matrix synthesis | 2× baseline |
| shADAMTS5 | ADAMTS-5 expression | 90% knockdown |
| shMMP13 | MMP-13 expression | 85% knockdown |

### Monte Carlo Simulation

- Number of iterations: 1,000
- Parameter uncertainty: ±20% uniform distribution
- Initial conditions: Steady-state OA phenotype
- Simulation time: 12 weeks
- Integration method: Runge-Kutta 4th order
- Time step: 0.1 hours

### ECM Recovery Score Calculation

```
ECM_Score = (Collagen_II / Collagen_healthy) × 40 +
            (Aggrecan / Aggrecan_healthy) × 40 +
            (SOX9_activity / SOX9_healthy) × 20
```

Where `_healthy` denotes the value in normal cartilage homeostasis.

All simulations were implemented in Python 3.9 using NumPy, SciPy, and Pandas. Code is available from the corresponding author upon reasonable request.

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## Supplementary Figures

**Supplementary Figure S1.** Gene Expression Heatmap from Network Simulations.
Heatmap depicting relative expression levels (0.0–1.0) of inflammatory mediators (IL-1β, TNF-α, COX-2, MMPs, ADAMTS-5) and structural components (COL2A1, aggrecan, SOX9) across four conditions: control, IL-1Ra only, SOX9 only, and multi-target. Multi-target intervention shows coordinated suppression of catabolic and inflammatory genes with concurrent upregulation of anabolic markers, consistent with the highest ECM Recovery Score.

**Supplementary Figure S2.** Bootstrap Confidence Interval Distribution for Multi-Target ECM Recovery Scores.
Histogram of bootstrap mean ECM Recovery Scores from 100 resampled datasets under the multi-target intervention. The red dashed line denotes the observed mean (76.2), while orange dashed lines indicate the 95% confidence interval bounds, demonstrating narrow uncertainty and statistical robustness of the predicted benefit.

**Supplementary Figure S3.** Synergy Analysis – Observed Versus Expected Additive Effect.
Bar chart comparing the expected additive ECM Recovery Score (67.4) derived from IL-1Ra-only and SOX9-only interventions with the observed multi-target score (76.2). The red arrow highlights the synergy margin (+8.8 points), and the calculated synergy index of 1.13 indicates a 13% improvement beyond additivity, supporting genuine multi-target synergy rather than simple summation of effects.