蛋白质螺旋-无序转变的亚残基锐度揭示了空间-频谱不确定性极限
Spectral analysis of protein backbone geometry reveals abrupt helix--coil boundaries
AI总结：
通过分析蛋白质螺旋-无序转变的亚残基锐度，揭示了空间-频谱不确定性极限，研究发现螺旋段呈现近可积分、低熵的孤子状状态，而无序区域则表现出宽带构象噪声，统计分析表明几何转变宽度仅为0.145个残基，提供了Zimm-Bragg模型高热力学协同性的独立动力学对应。
摘要：
合作性螺旋-无序转变的边界直接影射蛋白质别构和构象动力学，但这些结构界面处持续存在的一个到两个残基的分配模糊性物理起源仍未解决。我们应用离散的Hasimoto映射，将三维蛋白质主链几何结构转化为一维离散非线性薛定谔有效势能，并分析其空间-频率波动。螺旋段显示近可积分、低熵的孤子状状态，而无序区域则表现出宽带构象噪声。对1986种蛋白质中超过19000个边界进行统计分析，揭示出几何转变宽度的中位数仅为0.145个残基，提供了Zimm-Bragg模型高热力学协同性的独立动力学对应。这种亚残基空间狭窄性表明了一种由Gabor不确定性原理支配的内在观测限制，即任何宏观的频谱探测器倾向于模糊微观的相边界，暗示结构生物学中的边界模糊性不仅仅是算法性的，而是反映了生物聚合物晶格固有的物理分辨率限制。
英文摘要：
The boundaries of cooperative helix--coil transitions influence protein allostery and conformational dynamics, yet the persistent one-to-two-residue ambiguity in their assignment remains poorly characterized. We apply the discrete Hasimoto map to translate three-dimensional C$_α$ backbone geometry into a one-dimensional discrete nonlinear Schrödinger effective potential and analyze its spatial-frequency structure. Helical segments appear as near-integrable, low-entropy states whose spectral power concentrates at the zero-frequency mode, whereas coil regions show broadband fluctuations. A pointwise integrability residual and a windowed spectral entropy separate the two phases with ROC AUC values of 0.783 and 0.715, and their combination reaches 0.803, while combining the residual instead with a low-frequency energy ratio reaches 0.815. Across 1\,986 proteins and 19\,148 of 21\,107 fitted helix--coil boundaries the transition is abrupt, with a median sigmoid width of 0.145 residues that measures the steepness of a single-step discrete jump rather than a literal sub-residue distance; the transition is directionally asymmetric, with helix exits sharper than entries. Across the full dataset every C$_α$ geometry-based assignment, including DSSP-calibrated P-SEA and both spectral probes, loses agreement with the DSSP hydrogen-bond reference most acutely at these boundaries, indicating that the assignment ambiguity is a general feature of C$_α$ geometry rather than any single algorithm. The windowed spectral probe is subject to a Gabor resolution limit and is therefore outperformed by the pointwise probe, which attains the lattice-limited resolution.
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