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Deep Signature: Characterization of Large-Scale Molecular Dynamics

Tiexin Qin, Mengxu Zhu, Chunyang Li, Terry Lyons, Hong Yan, Haoliang Li

TL;DR

The work tackles the challenge of extracting meaningful functional insights from large-scale molecular dynamics trajectories. It introduces Deep Signature, an end-to-end framework that combines soft spectral clustering for coarse-graining with a log-signature based representation of interatomic dynamics, followed by a classifier for molecular properties. The authors establish theoretical invariances and demonstrate superior performance across gene regulatory dynamics, EGFR mutation dynamics, and GPCR dynamics, illustrating improved capture of complex interatomic interactions. This approach offers a scalable, symmetry-aware tool with potential implications for drug discovery and the mechanistic understanding of protein function.

Abstract

Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose significant challenge for existing computational techniques. In this paper, we approach this problem for the first time by introducing Deep Signature, a novel computationally tractable framework that characterizes complex dynamics and interatomic interactions based on their evolving trajectories. Specifically, our approach incorporates soft spectral clustering that locally aggregates cooperative dynamics to reduce the size of the system, as well as signature transform that collects iterated integrals to provide a global characterization of the non-smooth interactive dynamics. Theoretical analysis demonstrates that Deep Signature exhibits several desirable properties, including invariance to translation, near invariance to rotation, equivariance to permutation of atomic coordinates, and invariance under time reparameterization. Furthermore, experimental results on three benchmarks of biological processes verify that our approach can achieve superior performance compared to baseline methods.

Deep Signature: Characterization of Large-Scale Molecular Dynamics

TL;DR

The work tackles the challenge of extracting meaningful functional insights from large-scale molecular dynamics trajectories. It introduces Deep Signature, an end-to-end framework that combines soft spectral clustering for coarse-graining with a log-signature based representation of interatomic dynamics, followed by a classifier for molecular properties. The authors establish theoretical invariances and demonstrate superior performance across gene regulatory dynamics, EGFR mutation dynamics, and GPCR dynamics, illustrating improved capture of complex interatomic interactions. This approach offers a scalable, symmetry-aware tool with potential implications for drug discovery and the mechanistic understanding of protein function.

Abstract

Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose significant challenge for existing computational techniques. In this paper, we approach this problem for the first time by introducing Deep Signature, a novel computationally tractable framework that characterizes complex dynamics and interatomic interactions based on their evolving trajectories. Specifically, our approach incorporates soft spectral clustering that locally aggregates cooperative dynamics to reduce the size of the system, as well as signature transform that collects iterated integrals to provide a global characterization of the non-smooth interactive dynamics. Theoretical analysis demonstrates that Deep Signature exhibits several desirable properties, including invariance to translation, near invariance to rotation, equivariance to permutation of atomic coordinates, and invariance under time reparameterization. Furthermore, experimental results on three benchmarks of biological processes verify that our approach can achieve superior performance compared to baseline methods.
Paper Structure (23 sections, 1 theorem, 21 equations, 10 figures, 8 tables)

This paper contains 23 sections, 1 theorem, 21 equations, 10 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methodology
  4. Problem Formulation
  5. Deep Signature
  6. Equivariance & invariance of log-signature
  7. Implementation
  8. Experiments
  9. Experiments on Gene regulatory dynamics
  10. Experiments on epidermal growth factor receptor mutation dynamics
  11. Experiments on G protein-coupled receptors dynamics
  12. Conclusion
  13. Proof for Properties
  14. Translation Invariance
  15. Rotation Invariance
  16. ...and 8 more sections

Key Result

Theorem 1

Let $\breve{\mathbf{X}}_t$ be a reparametrization of $\mathbf{X}$, then we have $\mathrm{Sig}(\breve{\mathbf{X}})=\mathrm{Sig}(\mathbf{X})$.

Figures (10)

  • Figure 1: An overview of our proposed Deep Signature method.
  • Figure 1: Comparisons of classification performance on gene regulatory dynamics. Results are averaged over 5 runs.
  • Figure 2: The architecture of deep spectral clustering module.
  • Figure 3: The architecture of path signature transform module.
  • Figure 3: Ablation study on different loss items for Deep Signature. We report accuracy and recall for performance evaluation.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Theorem 1