The cellular cytoplasm is a complex, heterogeneous environment (both spatially and temporally) that exhibits viscoelastic behavior. To further develop our quantitative insight into cellular transport, we analyze data sets of mRNA molecules fluorescently labeled with MS2-GFP tracked in real time in live Escherichia coli and Saccharomyces cerevisiae cells. As shown previously, these RNA-protein particles exhibit subdiffusive behavior that is viscoelastic in its origin. Examining the ensemble of particle displacements reveals a Laplace distribution at all observed timescales rather than the Gaussian distribution predicted by the central limit theorem. This ensemble non-Gaussian behavior is caused by a combination of an exponential distribution in the time-averaged diffusivities and non-Gaussian behavior of individual trajectories. We show that the non-Gaussian behavior is a consequence of significant heterogeneity between trajectories and dynamic heterogeneity along single trajectories. Informed by theory and simulation, our work provides an in-depth analysis of the complex diffusive behavior of RNA-protein particles in live cells.

Recently, single molecule-based superresolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically use image fitting that assumes an isotropic emission pattern from the single emitters as well as control of the emitter concentration. However, anisotropic single-molecule emission patterns arise from the transition dipole when it is rotationally immobile, depending highly on the molecule's 3D orientation and z position. Failure to account for this fact can lead to significant lateral (x, y) mislocalizations (up to ∼50-200 nm). This systematic error can cause distortions in the reconstructed images, which can translate into degraded resolution. Using parameters uniquely inherent in the double-lobed nature of the Double-Helix Point Spread Function, we account for such mislocalizations and simultaneously measure 3D molecular orientation and 3D position. Mislocalizations during an axial scan of a single molecule manifest themselves as an apparent lateral shift in its position, which causes the standard deviation (SD) of its lateral position to appear larger than the SD expected from photon shot noise. By correcting each localization based on an estimated orientation, we are able to improve SDs in lateral localization from ∼2× worse than photon-limited precision (48 vs. 25 nm) to within 5 nm of photon-limited precision. Furthermore, by averaging many estimations of orientation over different depths, we are able to improve from a lateral SD of 116 (∼4× worse than the photonlimited precision; 28 nm) to 34 nm (within 6 nm of the photon limit).

We demonstrate quantitative multicolor 3D subdiffraction imaging of the structural arrangement of fluorescent protein fusions in living Caulobacter crescentus bacteria. Given single-molecule localization precisions of 20–40 nm, a flexible locally-weighted image registration algorithm is critical to accurately combine the super-resolution data with <10 nm error. Simple surface-relief dielectric phase masks implement a double-helix response at two wavelengths to distinguish two different fluorescent labels and to quantitatively and precisely localize them relative to each other in 3D.

Numerous methods for determining the orientation of single-molecule transition dipole moments from microscopic images of the molecular fluorescence have been developed in recent years. At the same time, techniques that rely on nanometer-level accuracy in the determination of molecular position, such as single-molecule super-resolution imaging, have proven immensely successful in their ability to access unprecedented levels of detail and resolution previously hidden by the optical diffraction limit. However, the level of accuracy in the determination of position is threatened by insufficient treatment of molecular orientation. Here we review a number of methods for measuring molecular orientation using fluorescence microscopy, focusing on approaches that are most compatible with position estimation and single-molecule super-resolution imaging. We highlight recent methods based on quadrated pupil imaging and on double-helix point spread function microscopy and apply them to the study of fluorophore mobility on immunolabeled microtubules.

The asymmetric nature of single-molecule (SM) dipole emission patterns limits the accuracy of position determination in localization-based super-resolution fluorescence microscopy. The degree of mislocalization depends highly on the rotational mobility of SMs; only for SMs rotating within a cone half angle α > 60° can mislocalization errors be bounded to ≤ 10 nm. Simulations demonstrate how low or high rotational mobility can cause resolution degradation or distortion in super-resolution reconstructions.

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object’s motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics (“static error”) and motion blur due to finite exposure time (“dynamic error”) on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors.

Nanoscale localization of single molecules is a crucial function in several advanced microscopy techniques, including single-molecule tracking and wide-field super-resolution imaging 1. To date, a central consideration of such techniques is how to optimize the precision of molecular localization. However, as these methods continue to push toward the nanometre size scale, an increasingly important concern is the localization accuracy. In particular, single fluorescent molecules emit with an anisotropic radiation pattern of an oscillating electric dipole, which can cause significant localization biases using common estimators 2-5. Here we present the theory and experimental demonstration of a solution to this problem based on azimuthal filtering in the Fourier plane of the microscope. We do so using a high efficiency dielectric metasurface polarization/phase device composed of nanoposts with sub-wavelength spacing 6. The method is demonstrated both on fluorophores embedded in a polymer matrix, and in dL5 protein complexes that bind Malachite green 7, 8.

Nitrogen-vacancy (NV) quantum defects in diamond are sensitive detectors of magnetic fields. Due to their atomic size and optical readout capability, they have been used for magnetic resonance spectroscopy of nanoscale samples on diamond surfaces. Here we present a protocol for fabricating NV-diamond chips and for constructing and operating a simple, low-cost "quantum diamond spectrometer" for performing nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy in nanoscale volumes. The instrument is based on a commercially-available diamond chip, with an ion-implanted NVensemble at a depth of ~ 10 nm below the diamond surface. The spectrometer operates at low magnetic fields (~ 300 G) and requires standard optical and microwave components for NV spin preparation, manipulation and readout. We demonstrate the utility of this device for nanoscale proton and fluorine NMR spectroscopy, as well as for the detection of transition metals via ESR noise spectroscopy. We estimate that the full protocol requires 2-3 months to implement, depending on the availability of equipment, diamond substrates, and user experience. Introduction:Magnetic resonance spectroscopy of electrons and nuclei comprises a family of ubiquitous and essential analytical tools in modern chemical and biological research 1 . Electron spin resonance (ESR), also known as electron paramagnetic resonance (EPR), spectroscopy is a useful means for probing molecules possessing unpaired electrons, such as transition metal complexes and radicals 2 . (Bio)molecules that lack an unpaired electronic spin can be probed via ESR-active spin labels. Nuclear magnetic resonance (NMR), on the other hand, is a more widely utilized technique, as NMR-active nuclei (e.g., 1 H, 13 C, 14 N, and 31 P) are commonly encountered in organic and biological chemistry. The narrow spectral lines of NMR afford unprecedented information about molecular structure and dynamics. NMR is less sensitive than ESR, however, owing to the lower gyromagnetic ratios of nuclei compared to that of the electron. In fact, both NMR and ESR are relatively insensitive when compared to the state of the art in other analytical techniques like mass spectrometry or fluorescence microscopy. The low sensitivity of magnetic resonance is particularly challenging for life science applications, where biomolecules of interest commonly occur in small absolute quantities or concentrations. Thus, there is great interest in new techniques to increase the sensitivity of magnetic resonance spectroscopy 3-5 . One promising approach employs a magnetic sensor based on fluorescent quantum defects in diamond, such as nitrogen-vacancy (NV) color centers, enabling interrogation of sample volumes down to the nanoscale 6,7 , including single proteins 8,9 , single protons 10 and 2D materials 11 . In this protocol, we describe the procedure for generating NV-diamond sensor chips and the construction of a "quantum diamond spectrometer" for NMR and ESR of nanoscale samples placed on the diamond chip. Physical back...