离散Hasimoto映射的分段可积性用于分析和设计螺旋肽
Piecewise integrability of the discrete Hasimoto map for analytic prediction and design of helical peptides
AI总结：
本研究通过分析螺旋肽的分段可积性，利用离散Hasimoto映射实现高精度主链结构预测与设计，揭示扭率非均匀性是偏离可积性的主因。
摘要：
通过离散非线性薛定谔方程表示蛋白质主链几何结构，为生物结构与可积系统之间的理论联系提供了桥梁。尽管该框架的全局应用受到手性退化和非局部相互作用的限制，螺旋肽可以被建模为分段可积系统，在特定几何边界内离散Hasimoto映射仍然适用。我们通过分析映射（ϕ，ψ）→（κ，τ）将生化二面角与弗莱奈框架参数联系起来，针对50条螺旋肽链进行分析。这种转换是全局信息保持的，但在螺旋盆地内（中位数雅可比条件数31）是病态的，表明手性信息损失主要源于局部坐标压缩，而非拓扑奇点。利用从离散色散关系导出的局部可积性误差E[n]，我们显示偏离可积性的主要驱动因素是扭率非均匀性，而曲率保持刚性。该度量标准识别出可积岛屿，其中分析色散关系可对主链坐标进行亚埃精度（中位数RMSD 0.77 Å）的预测，从而实现一种分割策略，以隔离结构缺陷并修剪非可积终端模糊部分。仅评估这些可积岛屿，色散关系可为数据集的88%提取高精度结构核心。在定义的可积性区域内，逆主链设计是可行的，其中设计约束本质上减少为控制扭率均匀性。这些发现将Hasimoto形式化从定性描述推进到精确的定量框架，用于分析和设计局部蛋白质几何结构，限于分段可积性范围内。
英文摘要：
The representation of protein backbone geometry through the discrete nonlinear Schrödinger equation provides a theoretical connection between biological structure and integrable systems. Although the global application of this framework is constrained by chiral degeneracies and non-local interactions, helical peptides can be modeled as piecewise integrable systems where the discrete Hasimoto map remains applicable within specific geometric boundaries. We delineate these boundaries through an analytic mapping $(ϕ,ψ) \rightarrow (κ,τ)$ between biochemical dihedral angles and Frenet frame parameters for 50 helical peptide chains. This transformation is globally information-preserving but ill-conditioned within the helical basin (median Jacobian condition number 31), suggesting chiral information loss arises primarily from local coordinate compression rather than topological singularities. Using a local integrability error $E[n]$ derived from the discrete dispersion relation, we show deviations from integrability are driven predominantly by torsion non-uniformity, while curvature remains rigid. This metric identifies integrable islands where the analytic dispersion relation predicts backbone coordinates with sub-angstrom accuracy (median RMSD 0.77\,Å), enabling a segmentation strategy that isolates structural defects and trims non-integrable terminal fraying. Evaluating only these integrable islands, the dispersion relation extracts high-accuracy structural cores for 88\% of the dataset. Inverse backbone design is feasible within a defined integrability zone where the design constraint reduces essentially to controlling torsion uniformity. These findings advance the Hasimoto formalism from a qualitative descriptor toward a precise quantitative framework for analyzing and designing local protein geometry within the limits of piecewise integrability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
