Unveiling interatomic distances influencing the reaction coordinates in alanine dipeptide isomerization: An explainable deep learning approach

The present work shows that the free energy landscape associated with alanine dipeptide isomerization can be effectively represented by specific interatomic distances without explicit reference to dihedral angles. Conventionally, two stable states of alanine dipeptide in vacuum, i.e., C7(eq) (beta-sheet structure) and C7(ax) (left handed alpha-helix structure), have been primarily characterized using the main chain dihedral angles, phi (C-N-C-alpha-C) and psi (N-C-alpha-C-N). However, our recent deep learning combined with the "Explainable AI" (XAI) framework has shown that the transition state can be adequately captured by a free energy landscape using phi and theta (O-C-N-C-alpha) [Kikutsuji et al., J. Chem. Phys. 156, 154108 (2022)]. In the perspective of extending these insights to other collective variables, a more detailed characterization of the transition state is required. In this work, we employ interatomic distances and bond angles as input variables for deep learning rather than the conventional and more elaborate dihedral angles. Our approach utilizes deep learning to investigate whether changes in the main chain dihedral angle can be expressed in terms of interatomic distances and bond angles. Furthermore, by incorporating XAI into our predictive analysis, we quantified the importance of each input variable and succeeded in clarifying the specific interatomic distance that affects the transition state. The results indicate that constructing a free energy landscape based on the identified interatomic distance can clearly distinguish between the two stable states and provide a comprehensive explanation for the energy barrier crossing.