Simultaneous measurements of single-molecule positions and orientations provide critical insight into a variety of biological and chemical processes. Various engineered point spread functions (PSFs) have been introduced for measuring the orientation and rotational diffusion of dipole-like emitters, but the widely used Cramér-Rao bound (CRB) only evaluates performance for one specific orientation at a time. Here, we report a performance metric, termed variance upper bound (VUB), that yields a global maximum CRB for all possible molecular orientations, thereby enabling the measurement performance of any PSF to be computed efficiently (${\sim}1000 \times$ faster than calculating average CRB). Our VUB reveals that the simple polarized standard PSF provides robust and precise orientation measurements if emitters are near a refractive index interface. Using this PSF, we measure the orientations and positions of Nile red (NR) molecules transiently bound to amyloid aggregates. Our super-resolved images reveal the main binding mode of NR on amyloid fiber surfaces, as well as structural heterogeneities along amyloid fibrillar networks, that cannot be resolved by single-molecule localization alone.

中文翻译：

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单分子定向定位显微镜用于解决淀粉样蛋白原纤维之间的结构异质性。

对单分子位置和方向的同时测量可提供对各种生物学和化学过程的关键见解。引入了多种工程点扩展函数（PSF）来测量偶极型发射器的方向和旋转扩散，但是广泛使用的Cramér-Rao界（CRB）一次只能评估一种特定方向的性能。在这里，我们报告了一个性能指标，称为方差上限（VUB），它为所有可能的分子取向提供了全局最大CRB，从而使任何PSF的测量性能都能得到有效计算（$ {\ sim} 1000 \ times $比计算平均CRB更快）。我们的VUB显示，如果发射器靠近折射率界面，则简单的偏振标准PSF可提供稳定而精确的定向测量。使用此PSF，我们测量瞬时结合到淀粉样蛋白聚集体上的尼罗红（NR）分子的方向和位置。我们的超分辨图像揭示了淀粉样蛋白纤维表面上NR的主要结合方式，以及沿淀粉样蛋白原纤维网络的结构异质性，仅凭单分子定位是无法解决的。