Analyzing Peptide Torsional Dynamics: An Angular-Displacement PCA Pipeline for Short-Horizon Prediction from Molecular Dynamics

Analyzing the conformational dynamics of short peptides from molecular dynamics (MD) simulations remains challenging. The high dimensionality of torsional space and the periodic nature of dihedral angles complicate statistical analysis and dimensionality reduction. This work presents an integrated computational workflow that combines all-atom MD simulations with a multistage analytical framework to characterize torsional reorganization patterns. Our approach introduces an angular-displacement representation χ that resolves periodic discontinuities by focusing on frame-to-frame torsional changes rather than absolute configurations. This transformation yields variables suitable for linear analysis and acts as a high-pass filter, emphasizing rapid reorganization events over slow conformational drift. We analyze these transformed coordinates using spatiotemporal principal component analysis (PCA) to identify collective torsional patterns. To evaluate how different coordinate choices preserve dynamical information, we quantitatively compare raw dihedral angles, sine-cosine embedding, and the displacement representation χ using the VAMP score. This comparison reveals their complementary nature: sine-cosine coordinates capture slow conformational variability, while χ highlights rapid torsional reorganizations. Subspace convergence analysis confirms the stability of the reduced PCA representation within the simulation time scale. We apply the methodology to the DENV-2 peptide (CGYGLC) as a representative short system. Our approach identifies hierarchical patterns of torsional flexibility─characterized by a flexible central core and region-specific dynamics─and reconstructs short-term structural evolution with angular errors below 25% and RMSD values of 1.0-2.1 Å. The main contributions are (i) a geometry-aware angular-displacement representation that respects the periodic nature of torsional variables; (ii) a spectral characterization of the displacement transformation; (iii) a quantitative comparison of observable representations using the VAMP score; and (iv) a demonstration of short-horizon structural prediction from reduced dynamical subspaces. The workflow provides a computationally efficient framework for analyzing torsional reorganization dynamics in peptide simulations.