Research map / Probabilistic and scientific modeling / Molecules and proteins
Deep Signature: Characterization of Large-Scale Molecular Dynamics
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Introduces Deep Signature, a GNN-based soft spectral clustering coarse-graining module followed by log-signature transform and LSTM to classify protein/gene MD trajectories, with theoretical invariance properties.
Problem
Characterizing high-dimensional, large-scale molecular dynamics trajectories and interatomic interactions for predicting protein functional properties, where existing methods are either oversimplified, costly with system size, or ignore interatomic interaction dynamics.
Approach
Combine differentiable GNN-based soft spectral clustering for coarse-graining atomic trajectories with a path log-signature transform (iterated integrals) that captures interatomic interactions globally, and prove invariance/equivariance properties (translation, near-rotation, permutation, time reparameterization).
Key results
- On EGFR dynamics, Deep Signature reaches 69.33% accuracy and 21.27% recall, versus 64.93% accuracy for GraphLSTM and 67.47% for dihedral-angle features.
- On GPCR dynamics, Deep Signature reaches 58.00% accuracy and 43.30% recall, versus 53.47% accuracy for GraphLSTM.
- Ablation on EGFR shows accuracy of 67.60% with classification loss only, 67.97% with temporal consistency added, and 69.33% with all three losses.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Deep Signature instead of the strongest baseline | EGFR dynamics classification · EGFR dynamics | accuracy: 67.47 ±0.98 -> 69.33 ±4.78 | Helped |
| Use Deep Signature instead of the strongest baseline | EGFR dynamics classification · EGFR dynamics | recall: 20.80 ±10.47 -> 21.27 ±8.26 | Helped |
| Use Deep Signature instead of GraphLSTM | GPCR dynamics classification · GPCR dynamics | accuracy: 53.47 ±14.86 -> 58.00 ±4.17 | Helped |
| Use Deep Signature instead of GraphLSTM | GPCR dynamics classification · GPCR dynamics | recall: 38.13 ±13.19 -> 43.30 ±7.85 | Helped |
| Add temporal consistency loss L_t to classification loss L_c (ablation) | Deep Signature · EGFR dynamics | accuracy: 67.60% -> 67.97% | Helped |
| Add spectral clustering loss L_u instead of temporal consistency loss L_t (ablation) | Deep Signature · EGFR dynamics | accuracy: 67.97% -> 66.00% | Hurt |
| Set coarsening level to 5 instead of 50 (ablation) | Deep Signature · EGFR dynamics | accuracy: 69.33 ±4.78 -> 57.33 ±4.73 | Hurt |
| Set coarsening level to 100 instead of 50 (ablation) | Deep Signature · GPCR dynamics | accuracy: 58.00 ±4.17 -> 50.67 ±5.58 | Hurt |
| Set λ1 to 10.0 instead of 1.0 (ablation) | Deep Signature · EGFR dynamics | accuracy: 69.33 ±4.78 -> 59.60 ±8.34 | Hurt |
| Set λ2 to 10.0 instead of 0.01 (ablation) | Deep Signature · EGFR dynamics | accuracy: 69.33 ±4.78 -> 65.27 ±2.48 | Hurt |
| Set λ3 to 0.01 instead of 10.0 (ablation) | Deep Signature · EGFR dynamics | accuracy: 69.33 ±4.78 -> 58.93 ±1.71 | Hurt |
Surprising findings
- Recall on EGFR is low for all methods (best 21.27%), and the authors attribute high-accuracy/low-recall baselines to class imbalance effects.
- Replacing the temporal consistency loss with the spectral clustering loss slightly degrades accuracy (66.00%), which the authors attribute to hard assignments.
Limitations
- Overall accuracies are modest (58% GPCR, 69% EGFR) on small datasets (24-26 trajectories), and recall is low.
- Rotation invariance is only partial: the authors show only a fraction of log-signature elements (ratio (3M-1)/(3M+1)) are rotation-invariant.
- Evaluation covers only three datasets, one of which is synthetic.
Experimental setup
Datasets: gene regulatory dynamics (synthetic, Michaelis-Menten simulation) EGFR mutation MD trajectories (Amber, 24 trajectories) GPCR MD trajectories from GPCRmd (26 trajectories)
Benchmarks: gene regulatory dynamics EGFR mutation dynamics GPCR dynamics
Metrics: accuracy recall
Baselines: Dihedral angle C-alpha dihedral angle Head Tail Head & Tail GraphLSTM GraphTrans
Builds on: path signature normalized cut graph convolutional network Signatory
Closest papers by meaning
- TEMPO: Temporal Multi-scale Autoregressive Generation of Protein Conformational Ensembles (NeurIPS 2025 · similarity 0.86)
- UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules (ICML 2025 · similarity 0.86)
- Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional (ICML 2025 · similarity 0.85)
- Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings (NeurIPS 2025 · similarity 0.84)
- Simultaneous Modeling of Protein Conformation and Dynamics via Autoregression (NeurIPS 2025 · similarity 0.84)
- Symmetry-Driven Discovery of Dynamical Variables in Molecular Simulations (ICML 2025 · similarity 0.84)
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