Volumetric imaging of the 3D orientation of cellular structures with a polarized fluorescence light-sheet microscope

Abstract

Polarized fluorescence microscopy is a valuable tool for measuring molecular orientations in biological samples, but techniques for recovering three-dimensional orientations and positions of fluorescent ensembles are limited. We report a polarized dual-view light-sheet system for determining the diffraction-limited three-dimensional distribution of the orientations and positions of ensembles of fluorescent dipoles that label biological structures. We share a set of visualization, histogram, and profiling tools for interpreting these positions and orientations. We model the distributions based on the polarization-dependent efficiency of excitation and detection of emitted fluorescence, using coarse-grained representations we call orientation distribution functions (ODFs). We apply ODFs to create physics-informed models of image formation with spatio-angular point-spread and transfer functions. We use theory and experiment to conclude that light-sheet tilting is a necessary part of our design for recovering all three-dimensional orientations. We use our system to extend known two-dimensional results to three dimensions in FM1-43-labeled giant unilamellar vesicles, fast-scarlet-labeled cellulose in xylem cells, and phalloidin-labeled actin in U2OS cells. Additionally, we observe phalloidin-labeled actin in mouse fibroblasts grown on grids of labeled nanowires and identify correlations between local actin alignment and global cell-scale orientation, indicating cellular coordination across length scales.

Keywords: biophysical; imaging; inverse problem; polarized fluorescence microscopy.

Fig. 1.

Orientation distribution functions (ODFs) can model ensembles of oriented fluorophores that label biological structures, their excitation, and their detection. (A) (i) Fluorescent samples consist of molecules that move and rotate in three dimensions (e.g. green fluorescent protein molecules pictured), and many of the most common fluorescent molecules’ excitation and emission behavior can be described by a single 3D dipole axis (double-sided black arrows overlaid on each molecule). Our instrument excites and measures emissions from diffraction-limited regions that contain many fluorescent molecules (dashed circle), so (ii) we simplify our model of individual emitters to a coarse-grained model called an object ODF. An ODF is a spherical function that we depict as a surface with a radius proportional to the number of dipoles in the measurement volume that are oriented along each direction. (B) Dipole distributions (Top row) can be modeled by object ODFs (Bottom row). (i) Fluorescent dipoles in solution typically rotate rapidly during the measurement time of fluorescent microscopes, so the corresponding ODFs are isotropic, depicted as a surface with constant radius. (ii–iv) When fluorescent dipoles (green double-sided arrows) are spatially and rotationally constrained, their corresponding object ODFs report the orientation of labeled biomolecules. (C) We can probe an object ODF by exciting a subset of molecules with polarized light. For example, when (i) linearly polarized light (red arrow) illuminates (blue arrow) an (ii) isotropic object ODF, (iii) the resulting subset of excited molecules, which we call an excited ODF, will have a ${cos}^2\theta$ dependence where $\theta$ is the angle between the incident polarization and the excitation dipole moment of the individual fluorophores in the distribution. Selectively exciting molecules creates contrast between different object ODFs. (D) We can create more contrast by selectively detecting an excited ODF’s emissions. (i) An excited ODF (red glyph) emits a polarized emission pattern (red arrows, perpendicular to the emission direction) that is anisotropic (solid black line, radius is proportional to the emitted power along each direction) which encodes information about the excited ODF. Selectively detecting emissions with an objective (blue arrow) creates contrast between excited ODFs. (ii) The emission pattern in (i) is the sum ($\mathrm{\Sigma }$) of the emissions from each dipole (green double-sided arrow) in ($\in$) the excited ODF. (iii) Similar to (i), each dipole emits a polarized emission pattern that is anisotropic, with each dipole emitting in a ${sin}^2\varphi$ intensity pattern where $\varphi$ is the angle between the emission dipole moment and the emission direction. (E) Each dipole emitter (green arrow) creates a measurable orientation-dependent point spread function. For example, in a 4$f$ imaging system, where $f$ indicates a focal length, (i) a transverse dipole emitter creates a pattern similar to the familiar Airy disc, while (ii) an axial dipole emitter creates a donut-shaped point spread function (shown here with normalized maximum irradiance). Black and white dots indicate the same points in the profile and image views.

Fig. 2.

Polarized dual-view inverted selective-plane illumination microscope (pol-diSPIM) data together with a physics-informed reconstruction enables volumetric measurement of three-dimensional orientation distribution functions. (A) (i) We imaged our samples with an asymmetric pair of objectives, each capable of excitation and detection. (ii) Illuminating our sample (green) with a light sheet (blue) from the 0.67 numerical aperture (NA) objective and detecting the emitted light from the 1.1 NA objective allows us to make planar measurements of diffraction-limited regions. Modulating the illumination polarization (red arrows) allows us to selectively excite ODFs within each diffraction-limited region, and orthogonal detection allows selective detection. (iii) Excitation from the 1.1 NA objective and detection from the 0.67 NA objective creates additional selective-excitation and selective-detection contrast and complementary spatial resolution. Scanning the sample through these polarized light sheets allows orientation-resolved volumetric acquisitions with more isotropic spatial resolution than detection from a single objective. (B) We used spherical harmonic decompositions of ODFs to simulate, reconstruct, and interpret our designs. (i) An example ODF is decomposed into the sum of an infinite number of spherical harmonics with the 15 smoothest nonzero terms shown. (ii) Truncating the infinite sum (red box at Right) smooths the ODF while preserving its overall shape, demonstrating the angular resolution our instrument can recover. (iii) Removing more terms (five red boxes) distorts the ODF and increases its symmetry, demonstrating the effect of missing components in the spatio-angular transfer function. (C) (i) A simulated phantom of radially oriented ODFs on the surface of a sphere is used to (ii) simulate a dataset. Each volume is simulated with a different illumination objective (rows) and illumination polarization (columns, red arrows indicate polarization, Pol. $=$ Polarization), illustrating how selective excitation and detection (with optical axes indicated by white lines) results in contrast that encodes spatio-angular information. (iii) A physics-informed reconstruction algorithm allows us to recover (iv) ODFs in volumetric regions (Inset, a single ODF corresponding to a diffraction-limited volume). We reduce these reconstructions to lower-dimensional visualizations including (v) peak orientations, where the orientation and color of each cylinder indicates the direction along which most dipoles are oriented, and (vi) density, a scalar value indicating the total number of values within each voxel. We further summarize distributions of peak orientations with (vii) angular histograms, where the central dot indicates the viewing axis, and density with (viii) spatial profiles, where the colored profiles correspond to the circumferential profiles in (vi). Color bar labels refer to fractions of the maximum value.

Fig. 3.

Light-sheet tilting enables experimental recovery of second-order spherical harmonic coefficients and all peak orientations. (A) We found that our spatio-angular transfer function had “angular holes” when expressed in a basis of spherical harmonics aligned with the detection axes. Red boxes indicate null functions, spherical harmonics that are not passed to the detected data. (B) These angular holes correspond to the ambiguity between dipoles that bisect the optical axes of the two objectives (green arrows). Dipoles that are oriented along these two directions will be identically excited, giving rise to signals that cannot distinguish these orientations. (C) We added MEMS mirrors to each excitation arm, enabling light-sheet illumination in the typical straight-through configuration (blue rectangle with solid outline) and the new tilted configurations (blue rectangles with dashed outlines). Tilting the light sheet makes new polarization orientations (red arrows) accessible while illuminating the same positions in the sample. (D) (i) A schematic of our Six no tilt acquisition scheme, where the sample (green) is illuminated with light sheets (light blue) propagating parallel to the optical axes of the objectives (dark blue arrows) under three different polarization illuminations per light sheet (red arrows). (ii) Peak cylinder reconstruction from experimental data acquired from a giant-unilamellar vesicle (GUV), where color and orientation encodes the most frequent dipole orientation from within each voxel, spaced by 260 nm. We expect the dipole orientations to be everywhere normal to the GUV, but instead see a red stripe across the top of the reconstructed GUV (see red arrows). (iii–v) Slices through the peak cylinder reconstruction, with incorrect orientations marked with red arrows. (E) (i) A schematic of our Six with tilt acquisition scheme, which uses a view-asymmetric combination of polarization and tilted light sheets to acquire more angular information from six illumination samples. (ii–v) Peak cylinder reconstruction using tilted light sheets shows recovery of all peak orientations [see green arrows in (ii) and (iv)]. Each column of (D and E) uses a single coordinate system described below the column where ${\widehat{\mathbf{d}}}_A$ and ${\widehat{\mathbf{d}}}_B$ are the detection optical axes.

Fig. 4.

Reconstruction of GUV, xylem, and actin samples validate pol-diSPIM’s accuracy and extend known 2D orientation results to 3D. (A) A $\sim$6 $\mathrm{\mu }$m-diameter GUV labeled with FM1-43 with (i) ODFs and (ii) peak cylinders separated by 650 nm. Radial profiles through the density map (iv) are used to plot density (v and vi) generalized fractional anisotropy (GFA) as a function of distance from the center of the GUV. In regions with low density, the GFA is dominated by noise and background contributions, so we have marked these regions as “high uncertainty” (red background). (B) A xylem cell with its cellulose labeled by fast scarlet with (i) ODFs and (ii) peak cylinders separated by 1.56 $\mathrm{\mu }$m. ROIs (iv and v) show peak cylinders separated by 650 nm with overlaid profiles (blue, green, red lines) that pass through the center of their nearest fibers (see SI Appendix, Fig. S17 for profiles through density), with histograms (blue, green, and red correspond to profiles) showing recovered orientations that run parallel to their fibers within $\sim$15 degrees. (C) U2OS cells with actin labeled by phalloidin 488 with (i) ODFs and (ii) peak cylinders separated by 390 nm. (v) A different view of peak cylinders with overlaid profiles (light green, orange lines) that pass through the center of their nearest fibers (see SI Appendix, Fig. S19 for profiles through density), with histograms (light green and orange correspond to profiles) showing recovered orientations that run parallel to their fibers within $\sim$10 degrees. Each column’s camera orientation and orientation-to-color map is displayed in the Bottom row. See also, Movies 1–6. Color bar labels refer to fractions of the maximum value.

Fig. 5.

pol-diSPIM measurements of phalloidin-labeled 3T3 mouse fibroblasts grown on nanowires show dipoles oriented parallel to their nearest nanowires and reveal distinct out-of-plane dipole populations across the cell. (A) Reconstructed density maximum intensity projection of a cell grown on crossed nanowires, with hand-annotated wires measured from a wire-specific channel highlighted with red and green lines. ROIs (i–v) are outlined in color and examined in subsequent panels. Color bar labels refer to fractions of the maximum value. (B) Peak cylinders drawn every 780 nm in regions with total counts $>$ 5,000, colored by orientation (see Inset color hemisphere), with lengths proportional to the maximum diameter of the corresponding ODF. (C) Histogram of all peak cylinders with total counts $>$ 5,000 in each ROI. Bins near the edge of the circle indicate in-plane orientations, bins near the center indicate out-of-plane orientations, and dots mark the Cartesian axes on the histogram.

Fig. 6.

Measurements of 3T3 mouse fibroblasts grown on different nanowire arrangements show correlations between voxel-scale 3D orientational order of F-actin and cell-scale orientations. (A) Reconstructed density maximum intensity projections of three cell repeats (columns) grown on varying nanowire arrangements (rows) named “Single,” “Paired,” and “Crossed” (cartoons at Left). Wires are overlaid as red and green lines. Color bar labels refer to fractions of the maximum value. (B) We collected reconstructed peak directions in voxels that were $<$5 $\mathrm{\mu }$m from a wire and had total counts $>$ 5,000, calculated their parallelism and radiality with respect to their nearest wire (see Inset cartoons where the red dot indicates a wire, and blue arrows indicate the neighboring peak directions for strongly parallel and radial peaks), and plotted their mean (dots) and SD (error bars) for each cell and nanowire arrangement (colors). Additionally, we calculated each cell’s “Aspect Ratio,” the ratio of the largest and smallest eigenvalues of the cell’s moment of inertia tensor (with the reconstructed density as a proxy for mass). (C) We compared population means (horizontal black lines) with a $t$-test and marked $P<0.05$–significant differences with asterisks. (D) We compared our local voxel-wise parallelism and radiality metrics to the cell’s global aspect ratio. We found positive and negative correlations between the aspect ratio and the parallelism and radiality, respectively, indicating local-global correlations in cellular behavior. Colored dots match (C), the red line is a linear fit to all nine data points, and the annotated $r$ values are Pearson correlation coefficients.