BPS2026 – Compressed representations of protein vibrations using quantum-inspired tensor methods

Understanding the vibrational dynamics of proteins is fundamental to elucidating enzymatic mechanisms, conformational transitions, and allosteric communication pathways. Conventional approaches construct the Hessian matrix from molecular mechanics force fields and apply normal mode analysis (NMA). However, the quadratic memory requirements and cubic scaling of dense eigendecomposition impose severe limitations on the system sizes that can be investigated at atomic resolution. We present a quantum-inspired tensor framework for the efficient representation and analysis of protein Hessians in the 60–100 residue range. Cartesian Hessians are generated using CHARMM-based force fields, with solvent degrees of freedom excluded to focus on protein-intrinsic vibrational dynamics. The Hessians are reshaped into higher-order tensors and compressed into low-rank tensor formats. Matrix-vector products are evaluated through tensorized operators, and vibrational modes are extracted using Krylov-Lanczos subspace iteration restricted to targeted frequency windows. This formulation enables efficient recovery of vibrational eigenpairs and the reconstruction of infrared and terahertz spectra while preserving the essential spectral features of the dense reference. Accuracy is assessed through frequency comparisons, mode overlap metrics, and residue-resolved fluctuation profiles, with particular emphasis on low-frequency collective dynamics relevant to conformational flexibility. Beyond spectroscopy, the framework offers potential synergy with cryo-EM, where low-frequency modes provide a natural basis for interpreting conformational heterogeneity and guiding flexible density fitting. These results establish quantum-inspired tensor methods as a scalable and interpretable alternative to dense eigensolvers, extending high-resolution vibrational and spectroscopic analysis to biomolecular systems previously constrained by prohibitive computational cost.