Deep Signature: Characterization of Large-Scale Molecular Dynamics

2024-10-03

arXiv.org

AI Summary

Protein dynamics analysis faces modeling challenges arising from high dimensionality, nonsmoothness, and multiscale interatomic interactions. This paper introduces the first computationally tractable deep signature framework that integrates soft spectral clustering with the signature transform to establish a dual-scale dynamical representation paradigm. We theoretically establish that the framework satisfies key geometric invariances—including translation invariance, approximate rotation invariance, atomic permutation equivariance, and time reparameterization invariance. Leveraging geometric deep learning and trajectory embedding, our model achieves significant performance gains over state-of-the-art methods across three biophysical process benchmarks. It is the first method to jointly and robustly characterize both cooperative local aggregation and global nonsmooth dynamic interactions. This advances molecular mechanism interpretation and enables principled, geometry-aware intervention strategies for drug discovery and functional modulation.

Technology Category

• Machine Learning: Representation Learning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Characterize complex protein dynamics
• Reduce system size effectively
• Improve computational performance benchmarks

Innovation

• Soft spectral clustering reduces system size
• Signature transform characterizes global dynamics
• Deep Signature framework ensures computational tractability