Deep Signature: Characterization of Large-Scale Molecular Dynamics

Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex highdimensional 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. Biological processes are fundamentally driven by the dynamical changes of macromolecules, particularly proteins and enzymes, within their respective functional conformation spaces. Typical examples of such processes include protein-ligand binding, molecule transport and enzymatic reactions, and modern computational biologists investigate their underlying functional mechanisms by molecular dynamics (MD) simulations (Dror et al., 2012; Lewandowski et al., 2015). Built upon density functional theory (Car & Parrinello, 1985), MD has demonstrated remarkable capability in providing accurate atomic trajectories in three-dimensional (3D) conformational space and consist agreement with experimental observations (Frenkel & Smit, 2023). The computational analysis of MD data has been a subject of extensive research for decades, with the goal of characterizing systems from trajectory information.