Defining domain-specific orientational order in the desmosomal cadherins

Abstract

Desmosomes are large, macromolecular protein assemblies that mechanically couple the intermediate filament cytoskeleton to sites of cadherin-mediated cell adhesion, thereby providing structural integrity to tissues that routinely experience large forces. Proper desmosomal adhesion is necessary for the normal development and maintenance of vertebrate tissues, such as epithelia and cardiac muscle, while dysfunction can lead to severe disease of the heart and skin. Therefore, it is important to understand the relationship between desmosomal adhesion and the architecture of the molecules that form the adhesive interface, the desmosomal cadherins (DCs). However, desmosomes are embedded in two plasma membranes and are linked to the cytoskeletal networks of two cells, imposing extreme difficulty on traditional structural studies of DC architecture, which have yielded conflicting results. Consequently, the relationship between DC architecture and adhesive function remains unclear. To overcome these challenges, we utilized excitation-resolved fluorescence polarization microscopy to quantify the orientational order of the extracellular and intracellular domains of three DC isoforms: desmoglein 2, desmocollin 2, and desmoglein 3. We found that DC ectodomains were significantly more ordered than their cytoplasmic counterparts, indicating a drastic difference in DC architecture between opposing sides of the plasma membrane. This difference was conserved among all DCs tested, suggesting that it may be an important feature of desmosomal architecture. Moreover, our findings suggest that the organization of DC ectodomains is predominantly the result of extracellular adhesive interactions. We employed azimuthal orientation mapping to show that DC ectodomains are arranged with rotational symmetry about the membrane normal. Finally, we performed a series of mathematical simulations to test the feasibility of a recently proposed antiparallel arrangement of DC ectodomains, finding that it is supported by our experimental data. Importantly, the strategies employed here have the potential to elucidate molecular mechanisms for diseases that result from defective desmosome architecture.

Significance

Membrane-associated proteins facilitate an astonishing array of biological functions including signaling, molecular transport, respiration, and intercellular adhesion, among others. Many of these proteins assemble into large, intricate complexes to perform their cellular roles. Despite recent technical advances, elucidating the architecture of membrane-associated protein complexes remains a forefront challenge in cell biology. Herein, we investigate the molecular architecture of one such complex—the desmosome—using a combination of excitation-resolved fluorescence polarization microscopy and mathematical simulations. Our results provide novel insights into the difference between intracellular and extracellular organization of the transmembrane desmosomal cadherins. Importantly, the strategies employed here could be applied to a vast array of membrane-associated protein assemblies that are challenging to study with existing structural methods.

Introduction

Desmosomes are intercellular adhesive junctions that provide mechanical integrity to tissues that undergo large forces, such as epithelia and cardiac muscle (1,2,3,4,5). In addition to resisting mechanical stress, desmosomes have the unique ability to transition between distinct adhesive states (6): weaker, calcium-dependent adhesion, and a stronger, calcium-independent state known as hyper-adhesion (7). Dynamic conversion between these states allows cells to rapidly remodel during processes like wound healing, tissue differentiation, and development (1,3,6,8,9). Consequently, desmosomes act as key mediators of these events and are indispensable regulators of the balance between tissue strength and plasticity. Indeed, desmosomes are required for all vertebrate life (10), and dysfunction of their component proteins—when not embryonic lethal—can lead to severe disease of the heart and skin (1,11,12). Therefore, understanding the relationship between desmosome protein architecture and adhesive function is a challenge of critical importance relating not only to human health but also to our fundamental understanding of cell adhesion, proliferation, and differentiation. Despite the importance of desmosomes, their underlying molecular architecture remains elusive, owing in large part to their remarkable structural and functional complexity.

A single desmosome comprises hundreds of proteins from three distinct families (Fig. 1 A) (1,2,3,4,12). Desmosomal cadherins (DCs) are type I transmembrane proteins belonging to the cadherin superfamily of calcium-dependent cell adhesion molecules (13). DC ectodomains have four cadherin homology repeats (EC1–EC4) and a membrane-proximal extracellular anchor (EA) domain (14), each of which flank conserved calcium-binding motifs that act to partially rigidify the otherwise flexible protein (15). Adhesive binding between DC monomers from opposing cells involves the exchange of N-terminal β-strands, leading to the formation of strand-swap dimers (1,16,17). Many strand-swap dimers associate laterally to form the desmosomal adhesive interface, though the nature of those associations is poorly understood (3,5,16,17). DCs are subdivided into two types—desmogleins (Dsg1–Dsg4) and desmocollins (Dsc1–Dsc3)—based on the length and composition of their cytoplasmic tails, which are separated from the ectodomains by a short transmembrane α-helix (18). The three Dscs each include a longer “a” form and a shorter “b” form generated from the same gene by alternative splicing. The intracellular plaque proteins—plakoglobin (PG) and the plakophilins (Pkp1–Pkp3)—belong to the diverse family of armadillo (ARM) proteins and are characterized by a variable number of α-helical ARM repeats flanked by disordered N- and C-terminal segments (12). Sequential ARM repeats fold into versatile superhelices that enable interactions with multiple binding partners (19). In desmosomes, PG and the Pkps bind to the cytoplasmic tails of the DCs to form the outer dense plaque, though they also play diverse signaling roles throughout the cell (12,20). Finally, desmoplakin (DPI–DPII) belongs to the plakin family of cytoskeletal adaptor proteins (21). It is characterized by an N-terminal head, central rod, and C-terminal tail domain (12). The N-terminal head interacts with PG and the Pkps in the outer dense plaque, while the C-terminal tail binds to intermediate filaments, thereby forming the inner dense plaque and linking the desmosome to the cytoskeleton (12).

Figure 1.

Schematic of the desmosome and example images. (A) Stylized schematic of a single desmosome demonstrating approximate arrangement of component proteins and intermediate filament cytoskeleton. (B) Negative-stain transmission electron micrograph of a desmosome in cultured human keratinocytes (HaCaTs). (C) Widefield immunofluorescence images of A-431 cells stained for Dsg2 (top) and DP (middle), with a merged image shown at the bottom. A single desmosome is indicated with a circular ROI and is shown as a magnified inset.

While the major desmosomal proteins have been identified, the exact nature of their interactions within the desmosome remains controversial and poorly understood (4,8,11,12,14,18). This is due, in part, to a shortage of imaging techniques capable of probing protein architecture with molecular specificity. For example, although electron microscopy allows for the study of desmosome ultrastructure at the nanoscale (Fig. 1 B), it is inherently nonspecific (22). Conversely, optical techniques like conventional fluorescence microscopy enable investigation of the dynamics and localization patterns of specific proteins (Fig. 1 C) but are limited in spatial resolution by the Abbe diffraction limit (23). The challenges posed by these technical limitations are compounded by the complex expression patterns and interaction modes of the various desmosomal components. Except for PG, each desmosomal component includes multiple isoforms that are expressed in a tissue- and differentiation-dependent manner (1,10,11,12,20). Most of these proteins have multiple binding partners, and many of the interactions between desmosomal components involve intrinsically disordered domains that only become structured upon binding (1,3,5,12,18,24,25). These complexities have hindered attempts to relate desmosome architecture to adhesive function, as evidenced by the lack of a complete mechanism describing the transition between adhesive states (6,7,26). Similarly, many diseases linked to desmosome dysfunction lack an associated mechanism (11,12). Elucidating these mechanisms will ultimately require an understanding of the underlying architectural features that confer adhesion. Ostensibly, the adhesive properties of desmosomes are conferred primarily by the DCs. It is therefore likely that their spatial organization is a crucial determinant of adhesive function. Accordingly, many groups have attempted to define DC architecture using X-ray crystallography (4, 17), cryo-electron tomography (cryo-ET) (27,28,29), small-angle X-ray scattering (15, 30), and molecular dynamics simulations (28), among others (12). However, desmosomes are embedded in two plasma membranes, bound to two cytoskeletons, and are heterogeneous in both size and composition. Collectively, these factors impose extreme difficulty on traditional structural studies of DC architecture, which have yielded conflicting results (4,7,17,27,28,29).

To overcome these challenges, we employed excitation-resolved fluorescence polarization microscopy (FPM) to study DC architecture. FPM exploits the orientation dependence of fluorescence excitation, allowing for quantitative measurements of domain-specific orientational order in fluorescently labeled proteins. Previously, we used FPM to show that the most membrane-proximal extracellular domain of Dsg3 is ordered in a calcium-dependent manner (31,32). In this study, we measured and compared the order of the extracellular and intracellular domains of three DC isoforms, finding that the ectodomains are drastically more ordered than the cytoplasmic domains. The difference between intracellular and extracellular order was conserved across all DCs tested—including the ubiquitously expressed DCs Dsg2 and Dsc2—suggesting that it is an important feature of desmosomal architecture. Additionally, we employed azimuthal orientation mapping to show that DCs are arranged symmetrically about an axis perpendicular to the plasma membrane, consistent with several proposed models of DC architecture. Finally, we performed a series of computational simulations to test the feasibility of recently proposed models of DC ectodomain architecture (28), finding that the antiparallel model is compatible with our experimental data. Together, these results strengthen the controversial notion of highly ordered DC ectodomains that we and others have suggested previously while providing novel insights into the disparity between intracellular and extracellular DC domain organization.

Materials and methods

Cell culture and transfection

The epidermoid carcinoma cell line A-431 (ATCC, Manassas, VA, USA) was cultured in Dulbecco’s modified Eagle’s medium (DMEM) supplemented with 10% fetal bovine serum and 100 U/mL penicillin/streptomycin. Cells were maintained at 37°C and 5% CO₂. Prior to transfection, 25 mm no. 1.5 glass coverslips (Thorlabs, Newton, NJ, USA) were sonicated in 200 proof ethanol for 30 min. Sonicated coverslips were coated with 250 μL fibronectin at a concentration of 25 μg/mL, incubated for 45 min at room temperature (RT), and washed with 2 mL Hank’s balanced salt solution three times for 5 min each. Cells were then seeded into six-well plates containing the prepared coverslips and 1.5 mL serum- and antibiotic-free DMEM. Cells were transfected at 50% confluency using Lipofectamine 2000 (11668027; Thermo Fisher Scientific, Waltham, MA, USA). Immediately prior to transfection, 4 μg plasmid DNA and 10 μL Lipofectamine 2000 were diluted separately into 250 μL Opti-MEM-reduced serum medium (31985062; Thermo Fisher Scientific) for each well to be transfected. After incubating for 5 min at RT, the diluted DNA was added to the diluted lipofectamine and incubated another 20 min at RT. The prepared lipoplexes were added to each well, and the dish was gently mixed by shaking. After 4–6 h, media were replaced with supplemented DMEM. Cells were fixed 36–48 h after transfection with a 1:1 solution of ice-cold acetone and methanol for 10 min at 4°C. After fixation, cells were rinsed with 2 mL phosphate-buffered saline three times for 5 min each and stored at 4°C. Immediately prior to imaging, coverslips were placed in AttoFluor cell chambers (A7816; Thermo Fisher Scientific) containing FluoroBrite DMEM (A1896701; Thermo Fisher Scientific).

Constructs

The extracellular order probe for Dsg3, Dsg3-ECTO, was made by inserting EGFP between residues K499 and L615 of mouse Dsg3 (UniProt: O35902), replacing the membrane-proximal EA domain. The intracellular order probe, Dsg3-CYTO, was made by inserting EGFP between residues T639 and C640 of mouse Dsg3. The disordered control construct, Dsg3-LINK, was made by ligating the Dsg3 C-terminus to the N-terminus of EGFP with the flexible linker: ID(GGGGS)^×5TG. To design extracellular order probes for Dsg2, Dsc2a, and Dsc2b, a multiple sequence alignment was used to identify the residues that most closely corresponded to the EGFP insertion sites in Dsg3. EGFP was inserted between V503 and L610 of human Dsg2 (UniProt: Q14126) for Dsg2-ECTO, V582 and L692 of human Dsc2a (UniProt: Q02487-1) for Dsc2a-ECTO, and V582 and L692 of human Dsc2b (UniProt: Q02487-2) for Dsc2b-ECTO. A similar strategy was used for the intracellular order probes; EGFP was inserted between M634 and C635 of human Dsg2 for Dsg2-CYTO and between V715 and C716 of human Dsc2a for Dsc2a-CYTO. Disordered control constructs for Dsg2 and Dsc2a were made by ligating EGFP to the C-terminus of the proteins with the same flexible linker used for Dsg3. All residue numbers correspond to the full-length peptide prior to cleavage of the N-terminal signal sequence. Cloning of all Dsg3 constructs and Dsg2-ECTO was performed by the Emory Cloning Core (Emory University, Atlanta, GA, USA), as described previously (32). All other Dsg2 and Dsc2 plasmid sequences were built in SnapGene (San Diego, CA, USA) and cloned by VectorBuilder (Chicago, IL, USA).

Excitation-resolved FPM

Fluorescence polarization experiments were performed using a Nikon-Ti 2 microscope equipped with a motorized stage and a 60×, 1.49 numerical aperture oil-immersion objective. A continuous, 488 nm laser (Coherent, Santa Clara, CA, USA) operating at 15 mW was passed through a linear polarizer (Thorlabs) and an achromatic half-waveplate (AHWP10M-600; Thorlabs) before being focused on the objective back focal plane with a focusing lens (Thorlabs). The half-waveplate was placed in a motorized mount (PRM1Z8; Thorlabs) for digital control of the excitation polarization. The emission was passed through an emission filter (ET525/50m, Chroma) and captured on an ORCA-Flash 4.0 v.3 complementary metal-oxide-semiconductor camera (Hamamatsu, Hamamatsu City, Japan). The emission was collected in four-image stacks, 50 ms exposure per image, using excitation polarizations of 0°, 45°, 90°, and 135° with respect to the positive x axis in the microscope coordinate system. Prior to each experiment, three flat-field polarization stacks were taken at different locations on an autofluorescent plastic slide (92001; Chroma) and averaged along each excitation polarization angle to correct for uneven illumination across the field of view and between each polarization angle.

Expressions used to determine order factor and azimuth

The emission intensity (I) of a fluorophore excited with plane polarized light is proportional to the squared dot product of the excitation electric field vector ($\overrightarrow{E}$) and the absorption transition moment of the fluorophore ($\overrightarrow{\mu }$), such that

$$I\propto \left|\overrightarrow{E}{|}^2\right|\overrightarrow{\mu }{|}^2{\text{cos}}^2\left(\text{Ψ}\right)\text{,}$$ (1)

where $\text{Ψ}$ is the angle between $\overrightarrow{E}$ and $\overrightarrow{\mu }$ (33). When $\overrightarrow{E}$ is confined to the sample plane (x-y), Eq. 1 can be rewritten as

$$I\propto \left|\overrightarrow{E}{|}^2\right|\overrightarrow{\mu }{|}^2{\text{sin}}^2\left(\beta \right){\text{cos}}^2\left(\alpha -\omega \right)\text{,}$$ (2)

where α and β are the azimuthal and polar angles of $\overrightarrow{\mu }$ and ω is the counterclockwise rotation of $\overrightarrow{E}$ from the positive x axis (32,33). In a widefield optical configuration with a densely labeled sample, the peak-to-peak amplitude of the sinusoid represents the in-plane orientational order of many dipoles within a diffraction-limited spot, which we refer to as the order factor (OF). The phase of the sinusoid represents the orientation of the projection of the net dipole onto the sample plane, which we refer to as the azimuth.

To calculate the OF and azimuth, a stack of four emission images (R) was captured of the sample using excitation polarizations (ω) of 0°, 45°, 90°, and 135°. A corresponding flat-field stack (F) was collected prior to each imaging session. Image stacks are denoted by bold capital letters, while subsets of their elements are denoted by capital italics, for which indices i, j, and k denote a pixel in the ith row of the jth column of the kth image in the stack, where k is the set of linear indices corresponding to each polarization angle.

$$\mathbf{R}=\left(R_{ijk}\right)$$ (3)

$$\mathbf{F}=\left(F_{ijk}\right)$$ (4)

$$k=\left\{\omega /45+1\mid \omega \in \left\{0^{\circ }\text{,}{45}^{\circ }\text{, }{90}^{\circ }\text{, }{135}^{\circ }\right\}\right\}$$ (5)

Thus, $R_{111}$ signifies the intensity of a pixel in the first row of the first column of an image in stack R captured at an excitation polarization of 0°. F was normalized by dividing each element by the maximum value in the stack. We compensated for uneven laser illumination across the image and between excitation polarizations by dividing each element of R by the corresponding element of F, yielding the flat-field-corrected stack, C. Each set of four pixels in C was then normalized to its maximum value to obtain the normalized image stack, N.

$$\mathbf{C}=\left(R_{ijk}/F_{ijk}\right)$$ (6)

$$\mathbf{N}=\left(C_{ijk}/\underset{1\le k\le 4}{max}{C}_{ijk}\right)$$ (7)

OF and azimuth were determined from the intensity difference in each pair of normalized emission intensities captured at orthogonal excitation polarizations (32,34):

$$A=\left(N_{ij1}-N_{ij3}\right)$$ (8)

$$B=\left(N_{ij2}-N_{ij4}\right)$$ (9)

$$OF=\left({\left(A_{ij}^2+B_{ij}^2\right)}^{\frac{1}{2}}\right)$$ (10)

$$Azimuth=\left(\text{arctan}2\left(B_{ij}\text{, }{A}_{ij}\right)/2\right)$$ (11)

In this context, $\text{arctan}2$ is the four-quadrant inverse tangent function, which wraps phase values outside the normal range of the standard arctan function, $\left(-\pi /2\text{, }\pi /2\right)$, to yield a single unambiguous value in the range $\left[-\pi \text{, }\pi \right]$.

Image segmentation and object-oriented analysis

All post-acquisition calculations and image analysis were performed using a custom software package (Polarized Order Detection Software v.2.0) written in MATLAB (MathWorks, Natick, MA, USA). We began by computing the average intensity image, $I^{Avg}$, taken as the mean emission intensity across all excitation polarizations in the flat-field-corrected image stack, C. $I^{Avg}$ was eroded and then dilated with a disk-shaped structuring element, S, yielding the morphologically opened image, $I^{Open}$. To enhance the signal of small punctate structures, $I^{Open}$ was subtracted from $I^{Avg}$ to obtain $I^{Sig}$.

$$S=\left[\begin{array}{lllllll}0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 0\hfill \\ 0\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 0\hfill \\ 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill \\ 0\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 0\hfill \\ 0\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill & 1\hfill & 0\hfill & 0\hfill & 0\hfill \end{array}\right]$$ (12)

$$I^{Open}=I^{Avg}\circ S=\left(I^{Avg}\ominus S\right)\oplus S$$ (13)

$$I^{Sig}=I^{Avg}-I^{Open}$$ (14)

In the resulting signal-enhanced image, an intensity threshold was determined with Otsu’s method (35) to yield a binary mask representing regions of interest (ROI) to be analyzed. In certain cases of low signal-to-background (S/B) ratio, the threshold was further adjusted to only include punctate structures at cell borders. Finally, any regions identified by the mask that were either diffuse or not clearly localized to cell borders were removed manually with a user-defined ROI.

Once the mask was determined, it was used to segment the image into discrete objects. The pixel indices of each object were used to extract relevant object-specific values. A local background area for each object was determined using multiple dilations of the binary object mask. Because most masks did not encapsulate the low-intensity pixels at the edge of the object, a three-pixel-wide “buffer zone” was set around each object and excluded from S/B calculations. Signal and background values were measured from the raw, uncorrected data. First, the raw stack, R, was averaged along all excitation polarizations. The local background was then taken as the average raw pixel intensity in a two-pixel-wide zone around the buffer, while the local signal was taken as the average raw pixel intensity in the region defined by each object mask. In the minority of cases where the background pixels of one object overlapped with the signal or buffer pixels of another, those overlapping pixels were excluded from S/B calculations.

Statistical comparisons

All statistical comparisons of object OF distributions were made in GraphPad Prism (GraphPad Software, San Diego, CA, USA). Object OF values were pooled across multiple experiments and grouped according to the identity of the order probe. To control for unequal sample sizes and nonnormality, we employed the Kruskal-Wallis test as a nonparametric alternative to the ordinary one-way ANOVA. To make pairwise comparisons between individual groups, we used Dunn’s multiple comparisons test. We only compared OF distributions of constructs that were either generated from the same protein or represented the same DC domain. All resulting p values were adjusted for multiple comparisons, with p < 0.5 considered statistically significant.

Computational modeling of antiparallel and parallel order probe configurations

Mathematical simulations of order probe configurations were performed using a custom set of functions written in MATLAB (MathWorks). We used a cartesian coordinate system where the x-y plane and the z axis represented the sample plane and optical axis of the microscope, respectively. We modeled the orientation of order probe transition dipole moments (TDMs) based on two recently proposed arrangements of cadherin ectodomains: antiparallel and parallel (28). In the antiparallel model, cadherin ectodomains from each cell are organized into antiparallel rows; each row is rotated 180° about the membrane normal with respect to adjacent rows on the same cell. Cadherin ectodomains from the opposing cell are rotated 90° with respect to those on the first cell. Four dipoles were needed to represent all possible cadherin orientations in this context. In the parallel model, cadherin ectodomains are organized into parallel rows; all the cadherins from each cell have the same orientation, and cadherins from the opposing cell are again rotated 90° with respect to those on the first cell. Two dipoles were needed to represent each unique cadherin orientation in the parallel model. Dipoles were all modeled as Euclidean vectors of equivalent magnitude. For our purposes, the dipoles were arranged such that the x and y axes corresponded to the membrane and membrane normal, respectively.

Each antiparallel set of dipoles was constructed from a single reference dipole, ${\overrightarrow{\mu }}_1$. To properly orient ${\overrightarrow{\mu }}_1$ at some $\left\{\alpha \text{, }\beta \right\}$, a unit vector of the z axis was rotated about the y axis by angle β, then rotated around the z axis by angle α, such that

$${\overrightarrow{\mu }}_1=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0\\ \sin \alpha & \cos \alpha & 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\text{.}$$ (15)

Once properly oriented at some $\left\{\alpha \text{, }\beta \right\}$, ${\overrightarrow{\mu }}_1$ was rotated about the y axis by 180° to produce the symmetrically related dipole from the same cell, ${\overrightarrow{\mu }}_2$. Finally, the two dipoles of the opposing cell were generated by rotating ${\overrightarrow{\mu }}_1$ and ${\overrightarrow{\mu }}_2$ about the x axis by 180° and the y axis by 90°.

$${\overrightarrow{\mu }}_2=\left[\begin{array}{ccc}-1& 0& 0\\ 0& 1& 0\\ 0& 0& -1\end{array}\right]{\overrightarrow{\mu }}_1$$ (16)

$${\overrightarrow{\mu }}_3=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ -1& 0& 0\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& 0\\ 0& 0& -1\end{array}\right]{\overrightarrow{\mu }}_1$$ (17)

$${\overrightarrow{\mu }}_4=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ -1& 0& 0\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& -1& 0\\ 0& 0& -1\end{array}\right]{\overrightarrow{\mu }}_2$$ (18)

The following expressions were then used to determine $\left\{\alpha \text{, }\beta \right\}$ for each dipole in the set:

$$\alpha =\text{arctan}2\left(v\text{, }u\right)\text{and}$$ (19)

$$\beta =\text{arccos}\left(w\right)\text{,}$$ (20)

where u, v, and w are the x, y , and z components of each dipole, respectively.

For simulations incorporating orientational flexibility, each dipole was allowed to wobble within a cone of aperture, δ, with a vertex centered on the origin and an axis parallel to the dipole prior to wobbling. The orientation of each dipole within its cone was defined by orientation parameters φ, the rotation of the dipole about the cone axis, and θ, the tilt of the dipole with respect to the cone axis. In this context, the vector representation of each dipole after wobbling is obtained by

$${\overrightarrow{\mu }}_n=\left[\begin{array}{ccc}\cos \beta \cos \alpha & -\sin \alpha & \sin \beta \cos \alpha \\ \cos \beta \sin \alpha & \cos \alpha & \sin \beta \sin \alpha \\ -\sin \beta & 0& \cos \beta \end{array}\right]\left[\begin{array}{c}\sin \theta \cos \phi \\ \sin \theta \sin \phi \\ \cos \theta \end{array}\right]\text{,}$$ (21)

where α and β are the spherical coordinates of each dipole prior to wobbling. For each dipole, φ was drawn from a uniform random distribution, and θ was drawn from a truncated Gaussian distribution scaled to span the range $\left[-\delta /2\text{, }\delta /2\right]$. After wobbling, new $\left\{\alpha \text{, }\beta \right\}$ values were calculated by reapplying Eqs. 19 and 20.

At each experimental polarization angle, the average excitation probability of each antiparallel configuration was found by applying Eq. 2 to each of its four dipoles. For the parallel configurations, only dipoles ${\overrightarrow{\mu }}_1$ and ${\overrightarrow{\mu }}_3$ were considered. The OF and azimuth were then found by applying (8), (9), (10), (11), taking the average excitation probabilities as emission intensities. This process was repeated for each possible pair $\left\{\alpha \text{, }\beta \right\}$ for the reference dipole. The OFs and azimuths of each arrangement were recorded in a matrix and displayed as images. To assess the feasibility of different simulated configurations, we cross-referenced experimental OF data with the simulated OF data to produce heatmaps representing the most likely dipole orientations for each order probe. Simulations were performed under the assumption that the number of fluorescently labeled DCs contributed to a desmosome by each cell were equal. In reality, the relative contributions to individual junctions are unknown, and a minority of the desmosomes analyzed were formed between transfected and untransfected cells. Heatmaps for each ectodomain probe were then normalized and averaged together, yielding a single map representing the most likely orientations across all extracellular order probes. We narrowed down the range of possible configurations by excluding those whose azimuths were not perpendicular to the plasma membrane. From the resulting set of configurations, a single pair $\left\{\alpha \text{, }\beta \right\}$ with the highest probability was used to orient the crystal structure of EGFP, based on the experimentally determined orientation of its TDM (36). Finally, the rotations specified by (16), (17), (18) were used to orient three additional EGFP molecules to complete the antiparallel configuration. Visualizations of simulated EGFP orientations were produced using UCSF Chimera (37). Dipole configuration schematics were produced using a modified version of “3D Quiver with volumized arrows” from the MATLAB Central File Exchange (38).

Results

Object-oriented analysis of FPM data

To study DC architecture, we constructed a series of order probes (Fig. 2) designed to measure order in the extracellular and intracellular domains of three DCs: Dsg2, Dsc2, and Dsg3. In parallel, we constructed probes to act as disordered controls for each DC isoform (Fig. 2). DC order probes were expressed in A-431 cells and imaged with excitation-resolved FPM (Fig. 3 A). FPM relies on the well-established principle that the probability of exciting a fluorophore with plane polarized light is directly proportional to the mutual alignment of the absorption transition moment of the fluorophore, $\overrightarrow{\mu }$, and the electric field vector of the excitation light, $\overrightarrow{E}$, as described by Eq. 1 (34,39). Because excitation probability is directly proportional to emission intensity, the orientation of $\overrightarrow{\mu }$ can be determined by recording its intensity while varying the orientation of $\overrightarrow{E}$ (32,34,36,40,41,42,43). In a widefield setup with a fixed optical axis (Fig. 3 A), $\overrightarrow{E}$ is confined to the sample plane and can thus be described in a spherical coordinate system with a single angle, ω (Fig. 3 B). The orientation of $\overrightarrow{\mu }$ can be described with two angles: α, the orientation of the projection of $\overrightarrow{\mu }$ onto the sample plane, and β, the inclination of $\overrightarrow{\mu }$ relative to the z axis (Fig. 3 B). In this scenario—given by Eq. 2—the measured intensity of a fluorophore depends sinusoidally on both the difference between α and ω as well as the angle between the dipole and the propagation axis, β. In a densely labeled biological sample, the peak-to-peak amplitude of the intensity curve obtained by varying ω reflects the in-plane orientational order of many fluorophores within a single, diffraction-limited spot, a value we refer to as the OF. The phase of the curve, on the other hand, reflects the orientation of the projection of the average TDM onto the sample plane, henceforth referred to as the azimuth.

Figure 2.

Domain representation of order probes used in this study showing EGFP insertion sites for extracellular (ECTO), intracellular (CYTO), and control (LINK) constructs corresponding to Dsg2, Dsc2a/Dsc2b, and Dsg3. (A) (i) Dsg2-ECTO, (ii) Dsg2-CYTO, and (iii) Dsg2-LINK. (B) (i) Dsc2a-ECTO, (ii) Dsc2b-ECTO, (iii) Dsc2a-CYTO, and (iv) Dsc2a-LINK. (C) (i) Dsg3-ECTO, (ii) Dsg3-CYTO, and (iii) Dsg3-LINK.

Figure 3.

Overview of excitation-resolved fluorescence polarization microscopy (FPM) and object-oriented image analysis. (A) Schematic of the FPM optical path. (B) Excitation electric field vector ($\overrightarrow{E}$) and fluorophore transition dipole moment ($\overrightarrow{\mu }$) in spherical coordinates, where α and β correspond to the azimuthal and polar tilt angles of $\overrightarrow{\mu }$, respectively, and ω corresponds to the polarization angle. (C) Example emission stack (left) and resulting order factor (OF) image (right) of representative order probe, Dsc2b-ECTO. An example cell border is indicated with a rectangular ROI and shown as a magnified inset, with two individual objects labeled with a star and triangle. (D) (Top) Normalized emission intensity stack of the object labeled with a triangle in (C) (left) and resulting OF image (right). White arrows indicate the excitation polarization used to capture each image. (Bottom) Plot of emission intensity against excitation polarization. Individual pixels were normalized to the maximum value across all excitation polarizations and fit to a generic sinusoid (gray: individual pixel fits; blue: individual pixel azimuths; black: average of all pixel fits). (E) Same as (D) for the object labeled with a star in (C). (F) Average OF calculated for individual objects and the entire image in (C). (G) Segmentation of object triangle (top) and star (bottom) images into the signal and background regions used to determine local S/B. (H) Scatter plot of average OF versus local S/B for every object in the data set from which (C) was taken (n = 1,062 objects over 20 independent images). Data are colored according to S/B range (red: 1–2; green: 2–3; blue: 3–4; yellow: 4–5; magenta: 5–max). (I) Violin plot and statistical comparisons of the S/B ranges in (G). Bars represent Q1, median, and Q3. Significant differences between S/B groups were assessed with a Kruskal-Wallis test followed by Dunn’s multiple comparisons test. (^∗∗∗∗p < 0.0001; ^∗∗p < 0.01).

These principles can be exploited to study the spatial organization of fluorescently labeled proteins by quantifying the change in emission intensity as a function of ω. Upon expressing fluorescently labeled DC order probes in desmosome-forming cells, the OF and azimuth can be determined trivially from a series of emission images captured at excitation polarizations of 0°, 45°, 90°, and 135° by applying (3), (4), (5), (6), (7), (8), (9), (10). However, analyzing these data in a meaningful way poses several challenges. First, ROIs typically comprise many punctate, filamentous, or membranous structures that represent a relatively small percentage of the image area. As a result, many studies of this type have relied upon either an averaging approach, whereby pixel-wise calculations are performed on whole images and then averaged within an area of interest (44,45,46), or a manual selection approach, in which only a subset of image features are selected for detailed analysis (34). These approaches make it difficult to account for biological variability and to perform statistical comparisons. Additionally, accurate determinations of relative intensity changes are strongly dependent on the S/B ratio. Indeed, we have previously shown through mathematical modeling that accurate OF calculations are strongly dependent on high S/B levels, whereas low S/B levels lead to underestimation of the theoretical OF (32). Importantly, background intensity is not uniformly distributed in an image but instead fluctuates locally based on the illumination profile and specimen makeup (47), which may introduce bias when an image averaging approach is used.

We therefore developed an object-oriented analytical pipeline for our FPM data designed to ameliorate these potential biases. The strategy combines traditional intensity-based thresholding, morphological operations, and image segmentation to extract individual structures from an image and compute location-specific values. Fig. 3 demonstrates the value of such an approach, as applied to a representative subset of the experimental data. The example shown is for the construct Dsc2b-ECTO, in which EGFP has been inserted in place of the membrane-proximal EA domain of Dsc2b to report extracellular order (Fig. 2 B ii). A typical field of view (Fig. 3 C, left) contains many punctate structures, only some of which are desired for analysis. We employ a morphological masking strategy to identify desmosomal puncta localized to cell borders while excluding nondesmosomal structures in the cytoplasm. Once a suitable mask is obtained, the OF can be calculated for each pixel, displayed within the mask (Fig. 3 C, right), and then averaged across all pixels to obtain an image-average value. However, the OF can vary significantly between individual objects in an image (Fig. 3, D and E), rendering this approach incapable of representing the full distribution of the data. While the image-average OF is comparable to the mean object-average OF, it ignores the inherent variability between objects (Fig. 3 F). At least some of this variability could result from differences between the local environments of each object. For example, an object with relatively low background intensity and high S/B had an observed OF comparable to the population mean (Fig. 3 D), while an object with low S/B had an OF that fell well below the population mean (Fig. 3 E), despite only being separated by roughly 5 μm in the image (Fig. 3 C). However, it is impossible to determine whether object-to-object differences are due to local background fluctuations or are the result of true biological variability, making it difficult to perform meaningful quantitative comparisons. For this reason, we sought to determine the effect of local background fluctuations on observed OF.

We began by calculating the local S/B for each object in the data set. First, we defined regions representing the local signal and background of each object. The signal was defined by the area of the object mask, while the background was defined as a two-pixel-wide region outside the mask (Fig. 3 G). Because most object masks did not include the low-intensity pixels at the edge of the object, a three-pixel-wide buffer zone was set between each signal and background region and excluded from S/B calculations. We determined the local S/B for each object by taking the ratio of the average pixel intensity in each region. To examine the relationship between OF and local S/B, we plotted the average OF as a function of local S/B for each object in the data set (Fig. 3 H). In general, objects with low S/B had a similarly low apparent OF, as predicted by our prior modeling (32). The data were binned into five distinct S/B groups to examine the quality of the OF distribution within each S/B range (Fig. 3 I). In the lower two groups (S/B < 3), distributions were highly nonnormal and significantly different. By contrast, the distributions in the upper three S/B groups (S/B ≥ 3) were roughly normal and not significantly different. Based on this analysis, we imposed a global S/B cutoff (S/B ≥ 3) to improve the quality of the data and increase the robustness of statistical comparisons.

The Dsg2 ectodomain is significantly more ordered than the cytoplasmic domain

We previously used FPM to study the order of the Dsg3 ectodomain, finding that it was ordered when incorporated into desmosomes in human keratinocytes (HaCaT) (32). In the present study, we first sought to determine whether this order was conserved more broadly among the Dsgs. We chose Dsg2 as a representative Dsg based on its ubiquitous expression throughout desmosome-forming tissues (18,48). An extracellular order probe for Dsg2 was constructed by inserting EGFP in place of the membrane-proximal EA domain (Fig. 2 A i). In this construct—termed Dsg2-ECTO—the fluorophore is constricted through its N- and C-terminal associations with Dsg2 such that its TDM reflects the orientation of the cadherin. A disorder control construct—Dsg2-LINK—was made by fusing EGFP to the C-terminus of Dsg2 with a flexible linker (Fig. 2 A iii). In this context, the rotational mobility offered by the linker ensures that the orientation of the EGFP is not conferred by the orientation of the DC.

To test whether the Dsg2 ectodomain was ordered, we transfected Dsg2-ECTO and Dsg2-LINK into A-431 cells. Cells expressing either construct were imaged using excitation-resolved FPM. Briefly, for each ROI, we captured a stack of images using excitation polarizations of 0°, 45°, 90°, and 135° and calculated the OF by applying (3), (4), (5), (6), (7), (8), (9), (10). Individual objects of interest in each image stack were located using a morphological masking approach and then filtered based on local S/B. For each object, the OF was averaged across all pixels defined by the mask and plotted as a single data point. As expected, the OF for Dsg2-ECTO (0.32 ± 0.11) (Fig. 4, A i and B i) was significantly greater than that of Dsg2-LINK (0.13 ± 0.05) (Fig. 4, A iii and B iii). Importantly, the mean OF observed for Dsg2-LINK is indistinguishable from the OF arising from Poisson-distributed noise, suggesting that the construct is truly disordered (Fig. S1).

Figure 4.

FPM imaging and comparative analysis of extracellular and intracellular domain order. (A) Representative average intensity (left) and OF images (right) of Dsg2-ECTO (i), Dsg2-CYTO (ii), and Dsg2-LINK (iii). Scale bars on cell border (top) and single object (bottom) images represent 4 and 1 μm, respectively. Images for each construct are all shown at the same scale. (B) Swarm plots of object OFs for each of the corresponding constructs in (A): Dsg2-ECTO (red; n = 178 objects), Dsg2-CYTO (yellow; n = 70 objects), and Dsg2-LINK (purple; n = 257 objects). (C) Representative images of Dsc2a-ECTO (i), Dsc2b-ECTO (ii), Dsc2a-CYTO (iii), and Dsc2a-LINK (iv). (D) Swarm plots of object OFs for each of the corresponding constructs in (C): Dsc2a-ECTO (red; n = 399 objects), Dsc2b-ECTO (red; n = 389 objects), Dsc2a-CYTO (yellow; n = 141 objects), and Dsc2a-LINK (purple; n = 253 objects). (E) Representative images of Dsg3-ECTO (i), Dsg3-CYTO (ii), and Dsg3-LINK (iii). (F) Swarm plots of object OFs for each of the corresponding constructs in (E): Dsg3-ECTO (red; n = 138 objects), Dsg3-CYTO (yellow; n = 145 objects), and Dsg3-LINK (purple; n = 82 objects). Bars indicate mean ± SD. Objects for each construct were pooled from ≥ 12 individual images. Objects with local S/B < 3 were excluded from the analysis. Statistically significant differences were assessed with a Kruskal-Wallis test followed by Dunn’s multiple comparisons test (^∗∗∗∗p < 0.0001; ^∗∗∗p < 0.001; ^∗∗p < 0.01; ^∗p < 0.05). Only significant differences between constructs corresponding to the same cadherin isoform are shown.

Although the structure and organization of DC ectodomains have been studied extensively using a diverse assortment of techniques (4,5,7,15,17,28,29,32), less is known about the DC endodomains, for which very little structural data exist (4,5). We wondered whether the order observed in the Dsg2 ectodomain would extend to the cytoplasmic tail. To that end, we designed an intracellular order probe—Dsg2-CYTO—by inserting EGFP between the transmembrane domain (TMD) and the membrane-proximal intracellular anchor (IA) domain of Dsg2 (Fig. 2 A ii).

To measure the intracellular order in Dsg2, Dsg2-CYTO was expressed in A-431 cells, imaged with FPM, and postprocessed in the same manner outlined above. Notably, the EGFP in Dsg2-CYTO is only 24 residues away from the EGFP in Dsg2-ECTO, leading us to predict that the order observed in the Dsg2 ectodomain would extend to the membrane-proximal region of the Dsg2 cytoplasmic tail. Surprisingly, we instead found that the Dsg2-CYTO OF (0.17 ± 0.05) (Fig. 4, A ii and B ii) was significantly less than that of Dsg2-ECTO (Fig. 4, A i and B i). Importantly, the OF for Dsg2-CYTO (Fig. 4, A ii and B ii) was still significantly greater than that of the disordered control (Fig. 4, A iii and B iii), suggesting that the cytoplasmic domain retains some order. Nevertheless, given the proximity of the tag locations in the intracellular and extracellular probes, the disparity in their respective OF suggests a drastic difference in DC domain organization between opposing sides of the plasma membrane.

Domain-specific order differences in Dsg2 are conserved in Dsc2

Upon observing the difference between intracellular and extracellular order in Dsg2, we wondered whether the same relationship would extend to the Dscs. Analogous to our rationale for selecting Dsg2 as a representative Dsg, we chose Dsc2 to represent the three Dscs because it is the only Dsc expressed in all desmosome-forming tissues (18). As with Dsg2, we designed extracellular, intracellular, and control probes for Dsc2: Dsc2a-ECTO was made by replacing the EA domain with EGFP (Fig. 2 B i), Dsc2a-CYTO was made by inserting EGFP between the TMD and the IA domain (Fig. 2 B iii), and Dsc2a-LINK was made by attaching EGFP to the C-terminus with a flexible linker (Fig. 2 B iv).

Unlike the Dsgs, Dscs lack the intracellular proline-rich linker, the repeat unit domain (RUD), and the Dsg-specific terminal domain, which collectively comprise the desmoglein-unique region (DUR) (49). Although the function of the DUR remains poorly understood, we predicted that its absence would lead to differences in OF when compared with Dsg2. However, despite these structural differences, the apparent organization of Dsc2 closely resembled that of Dsg2. Specifically, the OF for Dsc2a-ECTO (0.30 ± 0.09) (Fig. 4, C i and D i) was significantly greater than that of both Dsc2a-CYTO (0.17 ± 0.06) (Fig. 4, C ii and D ii) and Dsc2a-LINK (0.13 ± 0.04) (Fig. 4, C iv and D iv). Moreover, a comparison of each Dsc2 domain with the corresponding domains of Dsg2 did not reveal any significant differences (Table S1). These results indicate that the difference between intracellular and extracellular order is not a Dsg-specific phenomenon, further suggesting that the C-terminal domains in the DUR are not required for proper DC ectodomain organization.

In addition to lacking the DUR, Dscs differ from Dsgs in that they exist in two alternatively spliced forms: “a” and “b.” The longer “a” form lacks all domains C-terminal to the intracellular catenin binding site (ICS), while the shorter “b” form possesses a truncated ICS domain followed by a short, isoform-specific C-terminal sequence (18). Our initial examinations of Dsc2a showed no differences when compared with Dsg2 (Table S1). Because the truncation of the ICS domain renders Dsc2b unable to bind PG, we wondered whether the two Dsc splice forms may behave differently. Specifically, we asked whether the inability of Dsc2b to bind PG would lead to a change in ectodomain order. To answer this question, we constructed an extracellular order probe for Dsc2b—Dsc2b-ECTO (Fig. 2 B ii). We found that while the OF for Dsc2b-ECTO (0.27 ± 0.06) (Fig. 4, C ii and D ii) was significantly greater than both intracellular (Fig. 4, C iii and D iii) and control OF (Fig. 4, C iv and D iv) for Dsc2a, it was also significantly less ordered than the extracellular domains of Dsc2a (Fig. 4, C i and D i) and Dsg2 (Table S1). Importantly, Dsc2a and Dsc2b share identical ectodomains and differ only in the composition of their cytoplasmic tails. Thus, although the magnitude of the OF decrease is relatively small, it cannot be explained by extracellular interactions and must instead be related to the truncation of the ICS domain. Therefore, while our collective findings indicate that ectodomain order is predominantly a result of extracellular adhesive interactions, they also suggest that intracellular plaque interactions may play a minor role in organizing the DC ectodomains.

Domain-specific order differences are conserved in Dsg3

Because our previous examinations of Dsg3 focused on extracellular order, we wanted to know whether the difference between intracellular and extracellular order observed in Dsg2 and Dsc2 was also conserved in Dsg3. As before, the extracellular order probe for Dsg3—Dsg3-ECTO—was made by replacing the EA domain of Dsg3 with EGFP (Fig. 2 C i) (32). Likewise, Dsg3-CYTO was made by inserting EGFP between the consensus TMD and the IA domain (Fig. 2 C ii), and a Dsg3-specific disorder control construct—Dsg3-LINK—was made by fusing EGFP to the C-terminus of Dsg3 with a flexible linker (Fig. 2 C iii).

Each Dsg3 probe was expressed and imaged under the same conditions used for Dsg2 and Dsc2. The observed OF for Dsg3-ECTO (0.32 ± 0.12) (Fig. 4, E i and F i) was significantly greater than that of Dsg3-CYTO (0.18 ± 0.05) (Fig. 4, E ii and F ii). Additionally, both extracellular and intracellular OFs for Dsg3 were significantly greater than that of the disordered control, Dsg3-LINK (0.14 ± 0.06) (Fig. 4, E iii and F iii). While Dsg2 and Dsg3 share a high degree of sequence and structural homology in their ectodomains, they differ in the length and composition of their cytoplasmic tails (4,5,18). Most notably, the RUD of Dsg2 contains six repeats, whereas Dsg3 only has two (18). However, no significant differences were observed when the OF in each domain of Dsg3 was compared with the corresponding domain of Dsg2 (Table S1), suggesting that the number of repeats in the RUD does not play an appreciable role in ordering the Dsgs. Taken together, these results point to a clear disparity between intracellular and extracellular Dsg domain organization that manifests independently of the specific Dsg isoform.

DC ectodomains are arranged with rotational symmetry about the membrane normal

While the OF offers a quantifiable metric of in-plane orientational order, it does not reveal the underlying geometry of a complex. Therefore, to further explore the spatial arrangement of DC ectodomains, we mapped the azimuthal orientations of net TDMs for each object. Fig. 5 provides an overview of this analysis, as performed for Dsc2b-ECTO (Fig. 5, A–C) and Dsc2a-LINK (Fig. 5, D–F). Azimuth values were computed for each pixel using Eq. 11 and are shown as lines whose length and color correspond to the OF in the pixel from which they were derived. For the ordered construct—Dsc2b-ECTO—azimuth lines are relatively well aligned both within each object and between nearby objects (Fig. 5 B). While the OF is a measure of orientational order of the TDMs within a single pixel, the alignment of azimuth lines across multiple pixels in the same object (Fig. 5 C) suggests that DC ectodomain architecture is consistent throughout the entire junction. In stark contrast, the azimuths of Dsc2a-LINK are not well aligned either within single objects or between nearby objects, indicating a high degree of orientational disorder (Fig. 5, E and F). The relationships between emission intensity, excitation polarization, azimuth, and OF are summarized by comparing pixels within individual objects. While the Dsc2b-ECTO pixel azimuths generally agree and the intensity curves are mostly in phase (Fig. 5 C), the curves for Dsc2a-LINK are mostly out of phase and of much lower amplitude by comparison (Fig. 5 F). Quantification revealed that azimuthal disorder within individual objects was significantly lower for all ECTO constructs when compared with their respective disordered controls, consistent with OF measurements (Fig. S2).

Figure 5.

Azimuthal orientation mapping of desmosomal cadherin ectodomain order probes. (A) Example average intensity image with overlaid azimuth lines for the representative order probe, Dsc2b-ECTO. Each line is centered on a single pixel and represents the net orientation of TDMs within that pixel. (B) Magnified images of the rectangular ROIs in (A), showing the background-subtracted average intensity (left) and overlaid azimuth lines (right); line length and color correspond to the OF of a single pixel, as indicated by the key. A single object is highlighted by a circular ROI and shown as a magnified inset. (C) (Top) Emission intensity stack of the object circled in (B), normalized to the maximum value across all object pixels and excitation polarizations. White arrows indicate the excitation polarization used to capture each image. (Bottom) Plot of emission intensity against excitation polarization. Individual pixels were normalized to the maximum value across all excitation polarizations, and each four-pixel stack was fit to a generic sinusoid (gray: individual pixel fits; blue: individual pixel azimuths; black: average of all pixel fits). (D–F) Same as in (A)–(C) for the representative control construct, Dsc2a-LINK. (G–I) Average intensity images (left) and orientation of azimuth lines (right) of Dsc2b-ECTO in linear (G), “S-shaped” (H), and “C-shaped” (I) desmosomes. Dashed black lines indicate the midline of each desmosome. The average azimuthal orientations are −36.4° ± 5.4°, 22.5° ± 20.1°, and 11.0° ± 30.1° for linear, “S-shaped”, and “C-shaped” desmosomes, respectively.

Quantitative determination of net TDM orientations with respect to the plasma membrane requires knowledge of the orientation of the membrane itself, which is difficult to measure and may not reflect the orientation of the desmosome. Thus, to provide context to our azimuth measurements, we instead relied on qualitative observations of net TDM orientations with respect to the orientation of each desmosome. Most desmosomes were linear in appearance, and their azimuths were roughly perpendicular to a line drawn through the center of the junction (Fig. 5 G). However, we also observed two less-prevalent desmosome morphologies: “S-shaped” (Fig. 5 H) and “C-shaped” (Fig. 5 I), so named for their curved appearances. Strikingly, even in desmosomes with high degrees of curvature, azimuths were aligned perpendicularly to the tangent of each desmosome midline. This alignment was observed for all DC ectodomain order probes, leading us to conclude that individual EGFP TDMs are symmetrically arranged about the membrane normal. Importantly, this observation suggests that DC ectodomains are also arranged with rotational symmetry about the membrane normal.

FPM supports the antiparallel model of DC architecture

Recently, Sikora et al. combined cryo-ET and molecular dynamics simulations to study the organization of DC ectodomains (28). As with prior tomographic studies of desmosomes, the inherent flexibility of the DCs led to ambiguities in fitting cadherin crystal structures to the electron density maps. To account for these ambiguities, the authors proposed several models of DC architecture, the most likely of which were the antiparallel and parallel models. Of these, Sikora et al. concluded that their data were best explained by the antiparallel model, in which DC ectodomains are organized into regularly repeating, alternating rows (28). If cadherin ectodomains are arranged with either antiparallel or parallel geometry, the EGFP dipoles in our DC ectodomain order probes should share that same organization. While we cannot directly detect these geometries from ensemble measurements made in a diffraction-limited setting, we sought to simulate them to assess compatibility with our experimental data.

A schematic of the antiparallel model (Fig. 6 A) illustrates four unique dipole orientations—two per cell—that are related by twofold rotational symmetry about the membrane normal in a desmosome viewed along the optical axis. To understand whether our measurements were compatible with this model, we performed computational simulations to determine the theoretical OF from a minimal set of dipoles needed to represent all possible antiparallel arrangements. In brief, each simulation began with a single reference dipole (${\overrightarrow{\mu }}_1$) oriented at $\left\{\alpha \text{, }\beta \right\}$. The dipole was then rotated about the membrane normal by 180° to simulate the symmetrically related dipole from the same cell (${\overrightarrow{\mu }}_2$). Both dipoles were then rotated by 180° about an axis parallel to the membrane, followed by a 90° rotation about the membrane normal to produce the two dipoles from the opposing cell (${\overrightarrow{\mu }}_3$ and ${\overrightarrow{\mu }}_4$). In this way, each configuration of four dipoles is defined by the $\left\{\alpha \text{, }\beta \right\}$ of the reference dipole.

Figure 6.

Computational simulations of antiparallel and parallel dipole configurations. (A) Example schematic showing EGFP dipoles arranged with antiparallel geometry, viewed along the optical axis. Spherical coordinates of each dipole are listed below. (B) Simulated OFs for all possible antiparallel configurations, where α and β are the spherical coordinates of the reference dipole used to build the configuration. A dashed white line marks the “trough” separating the central and outer zones where OF = 0. (C) Average dipole orientation with respect to the plasma membrane for each antiparallel configuration, classified into two zones: parallel or perpendicular to the membrane. (D) Probability heatmap of the most likely antiparallel configurations made by cross-referencing experimental and simulated OF data. Dashed white line indicates transition between parallel and perpendicular. (E) Constrained probability heatmap excluding configurations in (D) that would not yield a net dipole perpendicular to the membrane, as indicated by (C). (F–J) Same as in (A)–(E) for the parallel model. (K) Spherical coordinate system used for flexibility simulations, where α and β are the azimuthal and polar angles of the cone axis in the microscopic reference frame; φ and θ are the azimuthal and polar angles of the dipole in the cone reference frame; and δ is the cone aperture. (L) Simulated OFs for all antiparallel configurations at varying δ using either 4 (top) or 200 (bottom) dipoles. (M) Mean OF error as a function of δ for simulations using 4 (blue) or 200 (red) dipoles. Solid line and shaded area indicate mean and SD, respectively.

For each antiparallel configuration, we calculated both the OF (Fig. 6 B) and the average dipole orientation with respect to the plasma membrane (Fig. 6 C). The simulated data indicate that while all OF values are possible, the rotational symmetry of the complex confines the average dipole to two possible orientations: either parallel or perpendicular to the plasma membrane. To determine which simulated configurations were compatible with our observations, we cross-referenced experimental ectodomain OF values with the simulated data to produce a heatmap of probable orientations (Fig. 6 D). Lastly, because net TDMs in our experimental data were overwhelmingly perpendicular to the plasma membrane (Fig. 5), we constrained the probability map by excluding configurations in which the net TDM would be parallel to the membrane, yielding a relatively narrow distribution of possible configurations with a distinct central peak representing the set of configurations with the highest probability (Fig. 6 E). Importantly, these simulations demonstrate that our experimentally determined OF and azimuth values could both reasonably arise from an antiparallel arrangement of DCs.

We next sought to test whether the parallel model (Fig. 6 F) was compatible with our experimental data. In the parallel model, all the dipoles from each cell have the same orientation, while dipoles from the opposing cell are rotated 90° with respect to those on the first cell. To assess the feasibility of this model, we performed the same set of simulations described for the antiparallel model. As expected, the lack of rotational symmetry in the parallel model leads to a simulated OF map that drastically differs from the antiparallel model (Fig. 6 G). Similarly, the simulated azimuth data show that only a very narrow set of parallel configurations could yield an average dipole that is perpendicular to the membrane (Fig. 6 H). We again cross-referenced experimental and simulated OF data to generate a probability heatmap (Fig. 6 I) and excluded configurations that would not yield an average dipole perpendicular to the membrane (Fig. 6 J). The map of allowed orientations shows that very few parallel configurations match both our OF and azimuth data.

These simulations show that only the antiparallel model can reasonably account for our observations. We next wondered whether this model could also explain the large range of experimentally observed OF values. Simulations performed thus far assumed a static arrangement of dipoles fixed in their orientations with respect to the target protein. However, the membrane-proximal DC domains are flexible, and there may also exist flexibility in the N- and C-terminal linkages between EGFP and the DC, both of which could impact the outcome of the simulations. To understand whether orientational flexibility could explain the large range of observed values, we repeated OF simulations of the antiparallel model while allowing each of the four dipoles to wobble freely within a cone of aperture, δ (Fig. 6 K). While the overall shape of the plot is maintained (Fig. 6 L, top), the mean OF error increases with higher degrees of flexibility (Fig. 6 M). When we repeated the simulations with 200 dipoles, a more realistic estimate of our experimental data (Fig. 6 L, bottom), the effect of flexibility is greatly diminished. (Fig. 6 M). These simulations suggest that while flexibility is not a significant source of error in simulations of the antiparallel model, it also fails to explain the range of observed values. We next asked whether the OF range observed could be explained by desmosomes with different orientations in the membrane (γ) (Fig. S3A). To address this, we calculated the OF range for each antiparallel configuration (defined by the orientation of ${\overrightarrow{\mu }}_1$ at $\gamma =0$°) as the complex made one full rotation about the membrane normal (Fig. S3B, left) and selected the $\left\{\alpha \text{, }\beta \right\}$ pair with an OF range that most closely matched the experimental data: $\left\{120\text{°}\text{, }120\text{°}\right\}$. The simulated OF range of this configuration (0.12–0.56) is very close to that observed experimentally (0.06–0.61). To assess the physical feasibility of this configuration, we arranged four EGFP molecules with antiparallel geometry by aligning their TDMs with those of the simulated dipoles (Fig. S4). The resulting EGFP positions suggest that this configuration is reasonable, as the N- and C-termini are oriented in a manner that would allow attachment to the DC ectodomain and the TMD, respectively. Taken together, these simulations indicate that our experimental OF and azimuth measurements support the antiparallel model of DC geometry.

Discussion

In this study, we investigated the spatial organization of extracellular and intracellular domains of three DCs using a series of chimeric order probe constructs expressed in A-431 cells and imaged with FPM. We showed that extracellular OF is significantly greater than intracellular OF despite the proximity of EGFP insertion sites, suggesting a drastic difference in DC architecture between opposing sides of the plasma membrane. This phenomenon was conserved across all three DCs tested—including the ubiquitously expressed Dsg2 and Dsc2—suggesting that it may be an important feature of desmosomal architecture. We further explored the arrangement of DC ectodomains using azimuthal orientation mapping. Our observations suggest that DC ectodomains are arranged with rotational symmetry about an axis perpendicular to the membrane, consistent with recently proposed models of DC architecture (28). Finally, we used computational simulations to show that our measurements are compatible with the antiparallel model of DC ectodomain architecture.

While it is now generally accepted that the DCs are arranged with some degree of regularity, the precise nature of their spatial organization within the desmosome remains somewhat controversial. Even ET studies, which offer the highest-resolution models of the desmosome to date, are often inconsistent or—in some cases—in direct conflict with each other. For instance, while some have suggested that DC ectodomains are stochastically clustered into discrete, unresolved groups resembling tangled knots (29), others have proposed a quasi-periodic arrangement consisting of regularly alternating cis and trans interactions (27). Although the reasons for these discrepancies are not completely clear, they are at least partially due to the inherent flexibility of the DCs, which imposes an upper limit on the spatial resolution that can be achieved, even when sub-tomogram averaging is used (28). More recently, Sikora et al. combined cryo-ET with molecular dynamics simulations to propose an antiparallel model of DC architecture that apparently reconciles many prior discrepancies (28). Notably, however, the high degree of flexibility in the DCs prevented resolution of densities corresponding to the most membrane-proximal extracellular domains. In the present study, we specifically targeted these regions by inserting EGFP between the transmembrane and EC4 domains. Although these domains could not be spatially resolved by cryo-ET, our FPM measurements suggest they retain orientational order despite their inherent flexibility. We supplemented our experimental measurements with a series of empirically driven mathematical simulations of the antiparallel model. By combining simulated and experimental FPM data, we bridged the gap with cryo-ET and showed that our observations support the notion of an antiparallel arrangement of DC ectodomains.

The object-oriented FPM approach used herein revealed broad diversity between individual junctions, which cannot be easily quantified with ET. While the source of these broad distributions remains unclear, our simulations suggest that the range of measured values could arise from desmosomes oriented differently in the plasma membrane. Alternatively, it may represent junctions in different biological states. Nevertheless, ectodomain OF was largely conserved between different DC isoforms despite the varying length and composition of their cytoplasmic tails. This suggests that DC ectodomain architecture is primarily driven by extracellular adhesive interactions, although the slight difference between Dsc2a and Dsc2b suggests that plaque interactions may also play a minor role. The finding of conserved ectodomain OF raises intriguing questions in two areas that remain unexplored: the impact of endogenously expressed cadherins and the interdependence between different DC isoforms. A-431s endogenously express both Dsg2 and Dsc2, as well as lesser amounts of Dsg3 and Dsc3 (50). Future studies are needed to investigate isoform-specific impacts on ectodomain architecture, such as whether the organization of Dsg2 depends on Dsc2, or vice versa. This would provide clarity on the effects of lateral clustering as well as the biological preference for either homotypic or heterotypic trans binding, neither of which are well understood.

While the architecture of DC ectodomains has been extensively investigated, little is known about the organization of DC cytoplasmic domains. Here, we show that the ECTO OF is significantly greater than the CYTO OF across all DCs tested, suggesting that DC cytoplasmic domains are less ordered than theirextracellular counterparts. Before discussing biological implications, there are several caveats to our measurements that need to be considered. First, because FPM relies on excitation with four distinct linear polarizations, any ellipticity or polarization mixing induced by the imaging setup will lead to systematic error and subsequent underestimation of the true OF. However, loss of polarization linearity would affect all samples equally and therefore cannot explain the large difference in OF between ECTO and CYTO constructs. Next, because the OF is a measure of in-plane orientational order, it also possible that these domains are highly ordered but predominantly oriented outside the measurement plane, which would cause underestimation of their true order. Another possibility is that our measurements could be confounded by flexibility in the linkages between EGFP and the DC. However, our flexibility simulations suggest that the difference between intracellular and extracellular OF cannot be explained by flexibility of the labeling alone. Moreover, the notion of highly ordered cytoplasmic domains is inconsistent with theoretical and experimental studies conducted by others. For example, structural studies of the catenin-binding domain of the adherens junction protein E-cadherin—which is closely related to the DCs—show that it is intrinsically disordered and only becomes structured upon binding PG (24). Sequence similarity suggests that a similar process likely occurs in the interaction between PG and DCs (12). Relatedly, solution studies of the poorly understood desmoglein-specific C-terminal region show that it is also intrinsically disordered (25). To the best of our knowledge, no ET study to date has been able to individually resolve the cytoplasmic domains of the DCs, inconsistent with a highly ordered architecture (27,28,29, 51).

Interestingly, one tomographic study of the desmosomal plaque suggested that the DC cytoplasmic domains were highly ordered, even though they could not be individually resolved (51). Notably, structures of the DC cytoplasmic domains were modeled using the homologous E-cadherin as a template, and the study relied heavily on subtomogram averaging. This hints at yet another intriguing possibility: that cytoplasmic order may not be homogeneously distributed throughout the desmosome. Because OF is an ensemble measurement, it is possible that cytoplasmic domains in the core of the desmosome are highly ordered, while those at the desmosome periphery are disordered and more mobile. This model would reconcile two apparently conflicting conclusions. A desmosome with predominantly disordered DC cytoplasmic domains would produce a low OF, even if the core was highly ordered. Conversely, in the tomographic study of the desmosomal plaque, subtomogram averaging and molecular modeling could lead to a model with highly ordered cytoplasmic domains, even if peripheral DCs were mostly disorganized. While we cannot presently distinguish between the various models of DC cytoplasmic organization, future studies employing imaging modalities that offer sub-diffraction-limited resolution or optical sectioning could provide more clarity to our findings. Still, our observations are not well explained in the context of other studies absent a difference in architecture between opposing sides of the plasma membrane.

The strongly conserved difference between extracellular and intracellular OFs may have functional importance, yet the biological implications remain unclear. Increasingly probable is the notion that highly ordered DC ectodomains are important for the maintenance of adhesion and resistance of mechanical stress. In fact, Sikora et al. posit that only a highly ordered antiparallel arrangement of DCs can adequately explain the biophysical properties of desmosomal adhesion (28). However, this fails to explain the dynamic properties of desmosomes, which can rapidly transition between distinct adhesive states and alter their plaque protein composition in response to cellular cues. For example, Pkp1 and Pkp3 play partially antagonistic roles during the transition between adhesive states; Pkp1 is required for the transition to calcium independence, whereas desmosomes with elevated levels of Pkp3 are more dynamic and unable to reach calcium independence (52). This finding is seemingly corroborated by the work of Fuchs et al., who showed that Pkp1, but not Pkp3, is required for the regulation of Dsg clustering (53). Interestingly, solution studies of the Dsg1 cytoplasmic tail have shown that while it is largely disordered, it may possess regions of inducible structure directed by binding to PG, DP, or Pkp1 (25). Together, these studies point to a potential mechanism for the modulation of adhesion by the plaque proteins, whereby the order of each DC cytoplasmic domain depends uniquely on its intracellular binding partners, which, in turn, confer distinct functional properties. In this sense, order in the DC cytoplasmic domains would vary throughout the desmosome, and the adhesive properties of the junction would result from the collective contributions of the various plaque proteins present.

Consistent with the idea of heterogeneous cytoplasmic order, Fülle et al. recently showed that the core components of the desmosome are highly stable, while Pkp2a remains persistently dynamic throughout the transition to hyper-adhesion: a form of “desmosome dualism” that would presumably be hindered by highly ordered DC cytoplasmic domains (54). This is consistent with earlier work from our own lab, which showed that DCs, PG, and DP all display reduced mobility upon the transition to calcium independence (31). It is becoming clearer that plaque protein exchange—and the modulation thereof—is a crucial aspect of desmosomal adhesive function that may be related to the transition between calcium-dependent and calcium-independent adhesive states. Therefore, one potential explanation is that the difference in ECTO and CYTO OFs represents a literal segregation of functional roles: highly ordered ectodomains provide adhesive strength and stability, while loosely packed cytoplasmic domains remain flexible enough to promote protein exchange and junctional remodeling.

Conclusion

In conclusion, our polarization experiments highlight a striking disparity between intracellular and extracellular domain organization in the DCs. The difference was consistent and conserved among three DCs—including the ubiquitously expressed Dsg2 and Dsc2—suggesting that it may be important for adhesive function. Meanwhile, our computational simulations provide experimental support for the recently proposed antiparallel model of DC ectodomain architecture. Together, our observations highlight the usefulness of fluorescence polarization techniques in structural cell biology. Ultimately, fully elucidating the architecture of intricate, membrane-bound protein assemblies like the desmosome will likely require a cross-platform correlative approach, wherein the high spatial resolution achievable through traditional structural methods is combined with the nanoscale specificity offered by techniques like FPM.

Author contributions

W.F.D. and A.L.M. designed the research and wrote the article. W.F.D. carried out experiments, analyzed data, and performed simulations.

Editor: Maria F. Garcia-Parajo.