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Generalized Implicit Neural Representations for Dynamic Molecular Surface Modeling
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Introduces MoE-DSR, a mixture-of-experts implicit neural representation with a geometric surface-cloud router and equivariant experts that predicts dynamic molecular surface SDFs for unseen proteins from ATLAS MD trajectories.
Problem
INRs that model dynamic protein surfaces via SDFs generalize poorly to unfamiliar protein families and ignore equivariance, limiting use as a surrogate for molecular dynamics simulations.
Approach
Combines a sparsely-gated mixture-of-experts with a router (GeoAN + quasi-geodesic message-passing network) that reads the initial static conformation, and experts that are equivariant implicit neural networks using spherical harmonics irreps, so that each expert specializes in protein subsets.
Key results
- MoE-DSR achieves overall IoU 0.7028, Chamfer distance 0.0039, and NC 0.6723 on ATLAS test, versus DSR at 0.5396, 0.0099, and 0.5788.
- Relative to DSR, MoE-DSR improves IoU by 30.24%, reduces CD by 39.40%, and improves NC by 16.15%.
- Replacing Q-MPNN with dMaSIF in the router gives IoU 0.6923, below MoE-DSR's 0.7028; removing the irreps/SH input drops IoU to 0.6884.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MoE-DSR instead of DSR | Dynamic surface reconstruction · ATLAS test (All) | IoU: 0.5396±0.0725 -> 0.7028±0.0390 | Helped |
| Use MoE-DSR instead of DSR | Dynamic surface reconstruction · ATLAS test (All) | Chamfer distance: 0.0099±0.0068 -> 0.0039±0.0019 | Helped |
| Use MoE-DSR instead of DSR | Dynamic surface reconstruction · ATLAS test (All) | NC: 0.5788±0.0532 -> 0.6723±0.0185 | Helped |
| Replace Q-MPNN with PointNet++ in the router (ablation) | MoE-DSR · ATLAS test (All) | IoU: 0.7028±0.0390 -> 0.6656 | Hurt |
| Replace Q-MPNN with PointCNN in the router (ablation) | MoE-DSR · ATLAS test (All) | IoU: 0.7028±0.0390 -> 0.6680 | Hurt |
| Replace Q-MPNN with Point Transformer in the router (ablation) | MoE-DSR · ATLAS test (All) | IoU: 0.7028±0.0390 -> 0.6749 | Hurt |
| Replace Q-MPNN with PointMLP in the router (ablation) | MoE-DSR · ATLAS test (All) | IoU: 0.7028±0.0390 -> 0.6857 | Hurt |
| Replace Q-MPNN with dMaSIF in the router (ablation) | MoE-DSR · ATLAS test (All) | IoU: 0.7028±0.0390 -> 0.6923 | Hurt |
| Replace equivariant irreps coordinate input with ordinary coordinates (ablation) | MoE-DSR · ATLAS test | IoU: 0.7028±0.0390 -> 0.6884±0.04 | Hurt |
| Increase the number of experts (ablation) | MoE-DSR · ATLAS test | IoU | No clear effect |
Surprising findings
- Increasing the number of experts beyond 16 does not improve performance, unlike MoE-based LLMs.
- A naive baseline that reuses the initial conformation for all timesteps achieves IoU 0.3375, indicating the task is non-trivial but the gap is informative.
Limitations
- Only single-chain monomer trajectories are modeled; protein complexes are not addressed.
- Experts specialize mainly on proteins with high sequence identity, and the training set is small (thousands of systems).
Experimental setup
Datasets: ATLAS
Benchmarks: ATLAS
Metrics: IoU Chamfer distance normal consistency
Baselines: DSR PointNet++ PointCNN Point Transformer PointMLP dMaSIF
Builds on: DSR sparsely-gated mixture-of-experts dMaSIF DeepSDF-style Eikonal loss
Closest papers by meaning
- AtomSurf: Surface Representation for Learning on Protein Structures (ICLR 2025 · similarity 0.87)
- Learning Over Molecular Conformer Ensembles: Datasets and Benchmarks (ICLR 2024 · similarity 0.86)
- Simultaneous Modeling of Protein Conformation and Dynamics via Autoregression (NeurIPS 2025 · similarity 0.85)
- AlphaFold Meets Flow Matching for Generating Protein Ensembles (ICML 2024 · similarity 0.85)
- Predicting directional flexibility in proteins (NeurIPS 2026 · similarity 0.85)
- Evaluating Representation Learning on the Protein Structure Universe (ICLR 2024 · similarity 0.85)
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