Painting rich six-dimensional pictures using polarized fluorescence microscopy

Cells organize biomolecules into a variety of architectures, both static and dynamic, to perform critical functions. Polarized fluorescence microscopy (1) is a versatile tool to visualize these structures in living cells, wherein the absorption and emission of polarized light by fluorescent molecules is directly measured to infer both their 3D positions and 3D orientations (2). For example, superresolved single-molecule orientation-localization microscopy (SMOLM) (3) has uncovered the architectures of actin filaments (4, 5) and membrane fluidity (6) in cells with nanoscale resolution but requires ~minutes to collect 10⁴ to 10⁵ single-molecule blinking events. Conversely, light-sheet imaging of molecular ensembles brings a dramatic increase in speed and reduction in phototoxicity at the cost of spatial resolution (7). However, polarized fluorescence microscopy faces longstanding challenges; summing overlapping signals from many molecules causes ambiguous orientation measurements, and unmixing position and orientation information is difficult without precise calibrations of the imaging system (8). A new polarized dual-view inverted selective-plane illumination microscope (pol-diSPIM), coupled with engineering insights provided by its imaging model, offers an exciting way forward (9).

In the companion article, Chandler et al. leverage a powerful mathematical model, developed from an image science perspective (10), to describe how both the positions and orientations of fluorophore ensembles impact the images produced by fluorescence microscopes, termed spatio-angular transfer functions (11). To begin, one may represent a set of fluorophore orientations using a distribution $f\left(\theta ,\varphi \right)$ defined on the surface of a unit hemisphere, where $\theta \in \left[{0,90}^{\circ }\right]$ and $\varphi \in [-{180}^{\circ },{180}^{\circ })$ represent polar and azimuthal angular coordinates, respectively (Fig. 1A). [Here, I simplify the authors’ model to consider imaging systems that probe a fluorophore’s absorption dipole or emission dipole but not both (3, 11).] Thus, an ensemble of molecules tumbling in solution is represented by a constant amplitude $f^{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}\left(\theta ,\varphi \right)=\frac{1}{2\pi }$ everywhere, while a set of molecules perfectly aligned with one another can be described by a single point, e.g., $f^{\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d}}\left(\theta ,\varphi \right)=\delta \left(\theta -{45}^{\circ }\right)\delta \left(\varphi \right)$ (Fig. 1A).

Fig. 1.

Principles of polarized dual-view inverted selective-plane illumination microscopy (pol-diSPIM). (A) Any set of molecular orientations may be represented as a distribution $f\left(\theta ,\varphi \right)$ on a unit hemisphere. Red: Dipoles aligned at $\left(\theta ={45}^{\circ },\varphi =0^{\circ }\right)$, purple: dipoles aligned at $\left(\theta ={45}^{\circ },\varphi =180^{\circ }\right)$, blue: dipoles uniformly distributed within a cone of solid angle $\mathrm{\Omega }=2\pi /3$ at a peak orientation $\left(\theta ={45}^{\circ },\varphi =0^{\circ }\right)$. (B) Normalized angular spectra $F_{\mathcal{l}}^m$ corresponding to orientation distributions in (A), where $f\left(\theta ,\varphi \right)={\sum }_{\mathcal{l},m}{F}_{\mathcal{l}}^m{Y}_{\mathcal{l}}^m\left(\theta ,\varphi \right)$. Any polarized fluorescence microscope that measures solely absorption or emission transition dipole moments is capable of measuring only $F_0^0,F_2^0,F_2^1,F_2^{-1},F_2^2$, and $F_2^{-2}$, which is termed the angular diffraction limit (11). (C) Spherical harmonics $Y_{\mathcal{l}}^m\left(\theta ,\varphi \right)$ plotted on the unit hemisphere corresponding to (A). (D) Schematic of pol-diSPIM with detection and illumination objective lenses; the roles of these lenses alternate during data collection. Three tilted and polarized light sheets (green) are shown with polarization vectors ${\mathit{E}}_1,{\mathit{E}}_2$, and ${\mathit{E}}_3$, which sequentially excite three distributions of dipoles, corresponding to (A). Gray line: optical axis of detection objective. (E) Simulated raw pol-diSPIM images of orientation distributions shown in (A), collected using tilted and polarized light sheets in (D). Top: green bar depicts path of beam ${\mathit{E}}_1$ and the focal plane of the detection objective. The leftmost three sets of dipoles are in focus, while the far-right set of red dipoles is defocused by 300 nm. Note that ${\mathit{E}}_1$ produces images of the red and purple distributions that are identical to one another and are also extremely similar to that of the blue cone distribution. Only after collecting images using tilted light sheets ${\mathit{E}}_2$ and ${\mathit{E}}_3$ can pol-diSPIM easily distinguish between these distributions. Defocused and aligned dipoles (red dipoles, 4th column) produce similar images to those of in-focus and wobbling dipoles (blue cone, 3rd column), illustrating spatio-angular coupling. Colorbars: (C) normalized amplitude, (E) normalized intensity. (Scalebar: 500 nm.)

By considering the angular diffraction limit (11), which is the orientation analog of the spatial optical diffraction limit, the authors demonstrate that any fluorescence microscope perceives a set of orientations $f\left(\theta ,\varphi \right)$ as a six-dimensional vector $F_{\mathcal{l}}^m$ (Fig. 1B), its so-called (discrete) angular spectrum. Mathematically, $F_{\mathcal{l}}^m$ represents the amplitudes of the spherical harmonics $Y_{\mathcal{l}}^m\left(\theta ,\varphi \right)$ with $\left(\mathcal{l},m\right)\in \left\{\left(0,0\right),\left(2,0\right),\left(2,1\right),\left(2,-1\right),\right.$ $\left(2,2\right),\left(2,-2\right)\}$ (Fig. 1C) that comprise.$f\left(\theta ,\varphi \right)$. (In SMOLM, fluorophore orientations have been represented as second-order moments of the transition dipole (12–14) and Stokes-Gell-Mann parameters (5, 15, 16); these are simply alternate bases to the spherical harmonics.) This representation is powerful for several reasons. First, this insight enables the authors to simplify greatly image reconstruction by estimating the six coefficients $F_{\mathcal{l}}^m$ (Fig. 1B) within each voxel instead of continuous functions $f\left(\theta ,\varphi \right)$ (Fig. 1A).

In the companion article, Chandler et al. leverage a powerful mathematical model, developed from an image science perspective (10), to describe how both the positions and orientations of fluorophore ensembles impact the images produced by fluorescence microscopes, termed spatio-angular transfer functions (11).

Second, the model permits the authors to elegantly contend with spatio-angular coupling, i.e., the mixing of spatial and angular information, within their microscope images. The authors experimentally calibrate their spatio-angular transfer functions for precise and accurate pol-diSPIM image reconstruction. They validate this analysis framework both in silico and experimentally and demonstrate robust estimation of peak orientations, i.e., the direction along which the greatest number of fluorophores are oriented, and generalized fractional anisotropy, the degree to which fluorophores exhibit a preferred orientation.

Perhaps the most impressive feature of the authors’ spatio-angular model is its ability to determine and characterize sets of fluorophore orientations that produce identical images; these orientational degeneracies manifest as holes in the spatio-angular transfer functions. Importantly, this issue cannot be solved by improving angular resolution, which is analogous to how distinguishing between an object $z$ nm above focus versus $z$ nm below focus cannot be solved by simply using an objective lens with a larger numerical aperture. Rather, the problem arises from dipolar symmetry; the probability that a fluorophore is excited is proportional to ${\cos }^2\eta$, where $\eta$ is the angle between the molecule’s dipole moment and the illumination polarization, and thus fluorophore angles $+\eta$ and $-\eta$ are indistinguishable. In the spatial case, one may break axial degeneracy by imaging near a refractive index interface or utilizing a suitably engineered point-spread function (1, 3). Here, the authors demonstrate that illuminating the sample with various tilted and polarized light sheets (Fig. 1D) breaks the angular symmetry and allows pol-diSPIM to distinguish between orientations that were previously ambiguous (Fig. 1E).

The authors demonstrate detailed orientational imaging of giant unilamellar vesicles, within which FM 1-43 fluorophores are oriented perpendicular to the membrane, and cellulose fiber organization at different regions within a xylem cell via the orientations of fast scarlet fluorophores. The authors also image the orientations of labeled phalloidin within a U2OS cell. Alexa Fluor 488 dipoles are nearly parallel (within ~10°) to actin filaments, which is consistent with SMOLM studies (4, 5).

The authors then characterize how actin organization at the sub-μm scale is related to that at the cellular scale within mouse fibroblasts. Extracellular matrix (ECM) fibers have been shown to influence actin stress fiber alignment, but how far this effect extends away from the membrane and into cells has not yet been studied. Here, the authors used ~200 nm-thick polystyrene wires, in single, paired, and crossed arrangements, to simulate the ECM and grew 3T3 fibroblasts directly on the scaffolds. Notably, orientation imaging directly quantifies the parallelism and radiality of F-actin fibers relative to the long axis of the wires, and these features can be examined voxel-by-voxel throughout each cell. The authors found that the fibers’ parallelism within cells grown on crossed wires was significantly different from those grown on single or paired wires. Similarly, cells on crossed wires showed significantly increased radiality compared to those on single wires. Overall, cells tended to be more elongated, i.e., exhibited a larger aspect ratio, with increasing F-actin fiber parallelism and decreasing fiber radiality, and thus, an ordered arrangement of polystyrene wires was observed to correlate with cell polarization. Chandler et al. provide the first direct quantification of how an anisotropic ECM network impacts local F-actin organization throughout entire cells.

In the context of cell imaging, dual-view, light-sheet microscopy has the advantage of greatly reducing phototoxicity and background autofluorescence compared to both widefield and confocal illumination. However, pol-diSPIM’s imaging speed (3.6 s per volume) currently limits its ability to study dynamics within living cells. Splitting the fluorescence into multiple polarized detection channels should improve pol-diSPIM’s imaging speed by requiring fewer tilt angles and polarization states to achieve sufficient measurement precision.

There are other insights to be gleaned by studying spatio-angular transfer functions; e.g., higher angular resolution can be achieved by using nonlinear light–matter interactions (17). In addition, given that a pair of fixed dipoles cannot be distinguished from a single wobbling dipole using polarized illumination or detection alone (18), the complementarity of SMOLM and pol-diSPIM in terms of spatio-temporal resolution and single-molecule vs. ensemble imaging will be important to consider and leverage. Distinguishing between fixed, disordered molecular arrangements and molecules whose rotational movements change in response to stimuli will be an important task for future polarization-sensitive imaging systems. Most importantly, there remains a continuing need for new methods to rigidly attach fluorescent molecules to their targets, so that their orientations match those of the biomolecule (1, 3, 19). All in all, exciting challenges and opportunities lie ahead for 6D imaging enabled by polarized fluorescence microscopy.