We develop six-dimensional single-molecule orientation-localization microscopy (SMOLM) to measure the 3D positions and 3D orientations simultaneously of single fluorophores. We show how careful optimization of phase and polarization modulation components can encode phase, polarization, and angular spectrum information from each fluorescence photon into a microscope’s dipole-spread function. We used the transient binding and blinking of Nile red (NR) to characterize the helical structure of fibrils formed by designed amphipathic peptides, KFE8L and KFE8D, and the pathological amyloid-beta peptide Aβ42. We also deployed merocyanine 540 to uncover the interfacial architectures of biomolecular condensates.
Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the CRB matrix from above; VUB overestimates the mean CRB by ~34%. However, compared to directly calculating the mean CRB over orientation space, we are able to calculate VUB ~1000 times faster.
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