Authors
Chuanyang Liu
Abstract
Proteins are not isolated structures but multilevel state spaces shaped by sequence and context. We introduce GRP, a general-relativity-inspired framework that treats AI representations as a lossy mirror space for searching for candidate invariants - relations intended to remain stable across models, coordinates and scales - and linking them to biological constraints. GRP formulates coordinate-aware geometric, tensorial and operator relations among empirical measures, covariance geometry, perturbational responses and distributional transport, providing an effective description of protein-state space. Across vast conformations and deep-mutational-scanning measurements from eight proteins, covariance spectra were concentrated, with 3-18 modes capturing 95% of retained variance; regularized inverse-covariance costs showed weak cross-resolution correspondence and modest fitness association. Biological descriptors predicted selected geometric responses, while structured paths showed lower Gaussian transport than matched nulls (11.75 versus 22.90). GRP is a testable statistical route from AI-observed organization to biological principles across proteins, nucleic acids, complexes and cells. Code and workflows are available at https://github.com/Travis13197/GRP.
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