Fig. 4: TS-DAR identifies transition states for alanine dipeptide.

a A representative conformation of alanine dipeptide. b Projection of the free energy landscape for alanine dipeptide onto two backbone torsion angles, \(\phi\) and \(\psi\). c Hyperspherical representations in a 3D latent space (2D hypersphere) for the 4-state TS-DAR model, with dashed lines indicating the centers of metastable states. d–f TS-DAR models with 2, 3, and 4 states successfully identified transition states located at different free energy barriers. Notably, for visualization, the molecular dynamics (MD) conformations with large out-of-distribution (OOD) scores (shown in yellow) are highlighted. g–i MD conformations with committor probabilities obtained from the 1,000-state Markov state model (MSM) overlaid with the free energy landscape mapped onto two backbone torsion angles. Notably, for visualization, the conformations with the committor probabilities between 0.4 and 0.6 are highlighted. The white regions represent the source and sink states, utilized as input into the transition path theory for computing committor probabilities. For further details, please refer to the SI Sec. 4. j–l Shannon entropy values of MD conformations obtained from 2, 3 and 4-state MaxEnt-VAMPNets³⁶ are shown. Source data are provided as a Source Data file.