发表机构
University Paris City; University of Reunion; ENERGYLab, University of Reunion; School of Information Science and Technology and Beijing Institute of Artificial Intelligence; Departamento de Ingeniería en Computación, Universidad de Magallanes; Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie; PEACCEL, AI for Biologics（巴黎城市大学; 留尼汪大学; 留尼汪大学能源实验室; 北京人工智能研究院及信息科学与技术学院; 麦哲伦大学计算机工程系; 勒阿弗尔诺曼底大学应用数学实验室（LMAH）; PEACCEL生物制剂人工智能公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对现有蛋白质构象表示无法保留形变顺序敏感信息的问题，提出基于四元数框架传输的非交换几何框架，可区分相似终态的有序形变历史，为相关分子生物研究提供新工具。
AI 中文摘要
蛋白质功能可能同时依赖于终态构象和达到该构象的有序形变历史，这种区分与别构效应、构象切换、突变诱导重排及上位效应相关——不同扰动序列可产生相似结构，但保留不同的内部传输历史。当前以状态或终态为中心的表示方法可能无法保留这种对顺序敏感的信息，因此本文为蛋白质形变轨迹的描述符提供基础，即使终态构象相似也能区分有序历史，这类描述符可用于分析别构切换、突变顺序效应、构象记忆及分子动力学轨迹、NMR系综、结构家族、几何生成模型输出中的路径依赖响应。本文提出一种基于蛋白质骨架上四元数框架传输的形变为先的几何框架，将局部骨架框架提升为四元数变量，无穷小旋转由\\\\(\Omega(\ell)=2\\,q(\ell)^{-1}\partial_\ell q(\ell)\\\\
英文摘要
Protein function may depend not only on endpoint conformations but also on the ordered deformation histories through which they are reached. This distinction is relevant to allostery, conformational switching, mutation-induced rearrangements, and epistatic effects, where different perturbation sequences may produce similar visible structures while retaining distinct internal transport histories. Current state-centered or endpoint-centered representations do not always preserve this order-sensitive information. The practical motivation is therefore to provide a foundation for future descriptors of protein deformation trajectories that can distinguish ordered histories even when endpoint conformations are similar. We propose a deformation-first geometric framework based on quaternionic frame transport along the protein backbone. Local backbone frames are lifted to quaternionic variables, with infinitesimal rotation encoded by \(Ω(\ell)=2\,q(\ell)^{-1}\partial_\ell q(\ell).\) Ordered concatenation of admissible deformation paths generates a noncommutative transport algebra, recording that deformation A followed by B need not be equivalent to B followed by A. From this ordered transport layer, we construct a spectral-response layer comprising a global Dirac-type operator, local spectral germs, a renormalized spectral density, and a mixed response form. A minimal realization on an idealized \(α\)-helix shows how localized pitch and bending perturbations can yield similar endpoint descriptors while producing a nonzero endpoint-derived ordered-transport discrepancy. At the formal level, the framework separates an order-sensitive transport-memory sector, lost under a commutative shadow, from a spectral-response sector that remains visible.
Comments43 pages, including 10 pages of appendices and 2 pages of references.5 figures. Submitted to Theory in Biosciences
