All Arabidopsis lines used in this study were generated in the Col‐0 background. Construction of all polarity protein reporter lines (pBRXL2::BRXL2‐YFP pML1::mCherry‐RCI2A, pBASL::YFP‐BASL pML1::mCherry‐RCI2A, pBASL::Myr‐BRX‐YFP pML1::mCherry‐RCI2A brxq, pBRXL2::BRXL2‐YFP pML1::mCherry‐RCI2A basl‐2, pPIN2::PIN2‐GFP) have been reported elsewhere (Wisniewska et al., 2006; Rowe et al., 2019). The Brachypodium BdYDA1 reporter line pBdYDA1::BdYDA1‐YFP was generated in the Bd21‐3 ecotype as described elsewhere (Abrash et al., 2018).

All Arabidopsis seeds were surface sterilised by bleach or 75% ethanol and stratified for 2 d. After stratification, seedlings were vertically grown on half½strength Murashige and Skoog (½MS) medium for 3–6 d under long‐day conditions (16 h : 8 h, light : dark, at 22°C).

All imaging experiments for Arabidopsis were performed on a Leica SP5 confocal microscope with HyD detectors using ×25 NA0.95 and ×40 NA1.1 water objectives with image size 1024 × 1024 and digital zoom from ×1 to ×2.5. For time‐lapse experiments, 3‐d post germination (dpg) seedlings were mounted in a custom imaging chamber filled with ½MS solution (Davies & Bergmann, 2014; Bringmann & Bergmann, 2017; Simmons et al., 2019). Laser settings for each reporter, except the membrane marker (pML1::mCherry‐RCI2A or PI), were adjusted to avoid over‐saturation. For the time‐lapse experiments reported in this study, 30 or 40 min intervals between each image stack capture were used.

Images of the BdYDA1 reporter in developing Brachypodium leaves were reanalysed from the same set of raw images reported in Fig. 3 of Abrash et al. (2018). Images of PAR dynamics in C. elegans embryos were reanalysed from the raw images of supplementary video 2 reported in Hubatsch et al. (2019).

All raw fluorescence image Z‐stacks were projected with Sum Slices in Fiji unless noted otherwise. For all time‐lapse images, drift was corrected using the Correct 3D Drift plugin (Parslow et al., 2014). These time‐lapse images were then split into individual time frames and treated as still images for analysis afterwards. Each individual cell of interest was then examined for manual correction before quantification, when regions containing interfering vesicles (images with FM4‐64 staining) or nucleus (images of BASL reporter) were manually removed. When running Pome (Supporting Information Methods S1) on a selected cell, the settings were adjusted per experiment. Information on how to determine Pome settings and examples of Pome data analysis are described in detail in the Pome user guide files (Notes S1, S2) accompanying this manuscript. The results of Pome measurement were then imported, summarised and analysed in RStudio.

For polarity proteins in Arabidopsis and Brachypodium stomatal lineage, the mean florescence intensity of the polarity protein reporter along the cell membrane was fitted to a Gaussian model (Eqn 1) by nonlinear regression with the nls function from the stats package (R Core Team, 2020) in rstudio. Key parameters of this regression model, including SD α, centre µ, amplitude α and baseline value β, were estimated using the formula: (Eqn 1)fx=αe‐12x‐μσ2+β

To determine if the parameters (σ, α and β) estimated by Pome were sufficient to distinguish between polarised (BRXL2 in stomatal lineage ground cells and BASL) and depolarised (BRXL2 in guard mother cells and Myr‐BRX) markers, we used measurements from 80 cells (20 cells per marker) to train a binary logistic regression model using the glm function from the stats package in rstudio. To visualise each parameter’s ability to classify polarity, a receiver operating characteristic (ROC) plot was generated with the roc function from the proc package (Robin et al., 2011). The resulting plot (Fig. 1h) suggest that σ alone could successfully discriminate between polarised and depolarised markers. Next, a simpler binary logistic regression model was built using only σ (Fig. 1i) to determine a suitable cut‐off value. To calculate the error rate of the polarity ~ σ logistic regression model, a 10‐fold cross‐validation prediction error was calculated with the training dataset with the cv.glm function in the boot package (Davison & Hinkley, 1997), where an average reporting error of 9.2% was reported.

For the support vector machine (SVM) model, the parameters from the same 80 cells in the binary logistic regression model were used as training data. To remove imaging setting and reporter basal expression bias, a normalised amplitude α′ was calculated by dividing the amplitude α by the mean fluorescence intensity of all angles. The SVM model was then built with the svm function in the e1071 package (Meyer et al., 2019). Next, linear coefficients were extracted from the model to calculate the slope (3.672) and intercept (0.069) of the decision boundary (Fig. S2b). We can then define an SVM polarity index as the distance to the SVM model decision boundary calculated with the formula:(Eqn 2)SVMpolarityindex=‐logeσ+3.672α′+0.069‐12+3.67222

A positive SVM polarity index indicates a polarised cell, while a negative SVM polarity index indicates a depolarised cell. Higher SVM polarity index values indicate higher polarisation.

All statistical analyses were performed in rstudio. Unpaired Mann–Whitney U‐tests were conducted to compare two data samples with the compare_means function from the ggpubr package (Kassambara, 2020).

The Arabidopsis stomatal lineage is a powerful model for genetic analysis of asymmetrical divisions, but mechanistic dissection of cell polarity has been challenging. BASL and BRXf polarity (demonstrated with BRX and BRXL2) is required for ACDs (Dong et al., 2009; Rowe et al., 2019), but how these proteins initiate and maintain polarisation is not understood. The primary challenge hindering quantitative analysis in the stomatal lineage is the rare and transient nature of cells undergoing ACDs, and demands the imaging of a large number of samples to discern statistically significant differences between genotypes or conditions. Additionally, cell shapes in the stomatal lineage are irregular and variable, which can make drawing conclusions from visual inspection difficult and adds uncertainty to manual measurements.

To reduce the time required for quantification and to collect shape‐agnostic measurements, we developed Pome, a pipeline composed of an intuitive Fiji macro and an R script that automatically extracted cortical polarity information from user‐defined cells. Pome requires confocal images of a cell with two different channels. One of these channels must contain a uniform cell outline marker (e.g. integral plasma membrane reporter, FM 4‐64 or propidium iodide). The macro then quantifies the fluorescence of polar proteins in the second channel at different angles (Fig. 1a–d). This simplification provides comparable results that are independent of cell shape. Users can specify the number of measurements (i.e. angles) along the membrane.

The macro calculates an angle of polarisation with respect to the field of view after extracting the centroid and the centre of mass of the polar protein in the measured cell from the outline marker and the polar protein channels, respectively. A line from the centroid to the centre of mass defines the 0° and 180° angles used for reporting results (Fig. 1b). Further analysis of these angles of polarisation could reveal the existence of tissue‐level coordination, as has been shown by previous studies (Bringmann & Bergmann, 2017; Mansfield et al., 2018).

Initially, we used Pome to quantify the distribution of BRXL2 in stomatal lineage ground cells (SLGCs) and found that its protein abundance at the membrane is well represented by a Gaussian model (Fig. 1e). This allowed us to describe the BRXL2 localisation with three parameters: SD, σ, amplitude (α) and baseline intensity (β) (Fig. 1e).

To evaluate the capacity of Pome to distinguish among degrees of polarity, we applied it to three additional cases: BASL (polarised), BRXL2 in guard mother cells (GMCs, depolarised) and myristoylated BRX (Myr‐BRX, depolarised) (Figs 1f,S1). These cases present a variety of challenges to polarity quantification, including signal interference from the nucleus (BASL), weak expression causing a low signal‐to‐noise ratio (depolarised BRXL2 in GMCs) and signals from abutting membranes in two neighbouring cells interfering with each other signals (myr‐BRX). We selected 20 cells for each marker and measured their distribution along the cell periphery. The distributions of these markers were different, but they can all be described by a Gaussian model (Fig. 1f). The SD, amplitude and baseline intensity (Fig. 1g) for BASL and the polarised BRXL2 were statistically indistinguishable (Fig. S2a). The distribution of the depolarised (cytosolic) BRXL2 and Myr‐BRX were clearly different from each other and from the distribution of the polarised BASL and BRXL2. Note that the SD of depolarised BRXL2 and Myr‐BRX were statistically indistinguishable, but their amplitudes and baselines were not, reflecting differences in fluorescence levels and possibly protein abundance (Fig. 1g).

Next, we compared the SD, amplitude and baseline intensity between our polarised and depolarised datasets using binary logistic regression and generated a ROC curve for each parameter to test its ability to classify polarity (Fig. 1h), where the closer the curve is to the upper left corner on the ROC plot, the higher the predictive power of the parameter. These results suggested that SD alone is predictive of polarity. Furthermore, SD is nearly independent of the expression level of the marker and the imaging setting, making it a reliable polarity classifier. To determine the cut‐off value for polarity classification using SD as the sole classifier, we plotted the sensitive (true positive rate) and specificity (true negative rate) for each SD cut‐off value. We found that a cut‐off of 42° can correctly discriminate between a polarised and a depolarised marker with a 95% classification sensitivity and 83% specificity, while a cut‐off of 60° achieved 100% classification sensitivity and 78% specificity (Fig. 1i,j). Alternatively, an SVM algorithm can be used to generate a polarity classification model with 100% classification sensitivity and 100% specificity using the SD and normalised amplitude (α′ amplitude divided by mean fluorescence intensity) (Fig. S2b,c).

We implemented Pome to analyse the dynamics of BASL and BRXf distribution. Biochemical studies indicated that BASL and BRXf interact, while genetic analysis indicated that they require each other to remain polarised (Rowe et al., 2019). BASL and BRXf have been shown to occupy the same general region of the cell cortex, but the evidence is limited to single time point images and qualitative interpretation. As a result, it is unclear if their polarity domains always overlap or whether one protein polarises first and then recruits the other.

To address this question, we first measured the distribution of BRXL2 before and after an ACD, from the initial formation of its polar crescent to its complete dissociation from the membrane (Fig. 2a). We fitted the fluorescence measurements of each time frame to a Gaussian model and extracted the SD, amplitude and baseline (Fig. 2b). We found that BRXL2 became polarised 5 ± 2.5 h before the formation of the new cell wall and remained polarised for over 9 ± 2.5 h afterward, using the SD cut‐off of 60° from our binary logistic regression. The SD and baseline values of the BRXL2 distribution remained remarkably constant over this period, while the amplitude increased and then decreased. This result could be consistent with scenarios in which BRXL2 is locally delivered to the crescent and retained there, or uniformly delivered to the membrane but transported into the crescent more rapidly than it can diffuse away.

Subsequently, we performed a similar characterisation of BASL dynamics. Comparison of the dynamics of BRXL2 and BASL showed that BRXL2 polarised earlier than BASL during ACDs and stayed polarised longer than BASL afterward (Figs 2c,S3). A dual‐reporter line expressing BRX‐CFP (a redundant homologue of BRXL2 in the stomata lineage) and BASL‐YFP further supported the hypothesis that BRXf polarises ahead of BASL during ACDs. In still images of the dual‐reporter line, from which we could obtain higher resolution images than in time‐lapse images, we identified a few cells at late G2/early mitotic phase where BRX, but not BASL, was polarised (Fig. 2d).

We also examined the dynamics of BRXL2 in basl‐2 null mutants, where BRXL2 was believed to be depolarised (Rowe et al., 2019). Strikingly, we found that, in some basl‐2 cells, BRXL2 could still polarise transiently during ACDs (Fig. 3a) and Pome could accurately describe these polarity changes (Fig. 3b). In these basl‐2 cells, BRXL2 was observed to polarise right after the formation of the cell wall that separates the new sister cells. This transient polarity coincided with the time window in which BRXL2 polarity is often enhanced in wild‐type cells (Fig. 3a,c,d). Whether this transient BRXL2 polar crescent in basl‐2 is functional, however, is debatable, as it did not show up in all the dividing cells and the basl‐2 mutant had evident ACD defects (Dong et al., 2009). Nevertheless, these results suggested that BRXL2 accumulates at the polar crescent first and then recruits BASL and the formation of this complex is required to retain both proteins at the crescent.

Pome was initially designed to address the challenges of measuring polarity in dispersed, asynchronously dividing, leaf epidermal cells. An automatic tool to quantify polarity, however, is useful for other developmental contexts and the simple design of Pome should make it adaptable to other tissues and organisms.

In Arabidopsis, the MAPKKK YODA (AtYDA) is polarised and segregated preferentially to larger daughter cells in the stomatal lineage ACDs by BASL (Zhang et al., 2015). In Brachypodium, a YODA homologue, BdYDA1, is also required for stomatal lineage ACDs (Abrash et al., 2018). However, the Brachypodium genome does not encode a BASL homologue (Bowles et al., 2020). It was therefore unclear whether BdYDA1 would be polarised in the Brachypodium stomatal lineage. Grass stomata are arranged in cell files and exhibit a base‐to‐tip gradient of development. Meristemoids undergo directional ACDs such that the smaller daughter cell (stomatal precursor, GMC) is oriented towards the tip and the larger one (pavement cell precursor) towards the base (Fig. 4a,b). To determine if BdYDA1 is polarised, we used Pome to quantify its distribution in individual meristemoids before ACDs and in the newly formed larger daughter cells resulting from this division (Fig. 4a,b).

BdYDA1 was not polarised in meristemoids but, after ACDs, polarised BdYDA1 was detected in the larger daughter cell (Fig. 4b,c). This segregation and polarisation of BdYDA1 is consistent with a role restricting stomatal fate and these larger daughters often wrongfully acquire stomatal identity in the loss‐of‐function mutant bdyda1 (Abrash et al., 2018). The position of polar BdYDA1, distal to the new division plane in the larger daughter cell, is equivalent to where AtYDA localises in a BASL‐dependent manner in Arabidopsis (Zhang et al., 2015). This leads to the interesting conclusion that MAPKKKs can and must polarise during stomatal ACDs to ensure differential fates in different plants, but BASL may be newly recruited into this role in dicots and alternative mechanisms must exist to polarise BdYDA1.

The expression of BdYDA1 in each of many contiguous stomatal cells represented a complication for automated polarity analysis. We had to rely on prior knowledge on oriented ACDs (Abrash et al., 2018) to infer in which cells and on what cell face BdYDA1 was localised. The problem of assigning polarity to individual contiguous cells is quite common. In Arabidopsis roots, for example, cells are also arranged in files and localisation of proteins to specific faces is required for the development and physiological functions of the root. Many proteins in the root and vascular systems, especially those involved in polar auxin transport, display polar localisation to ‘shootward’ and/or ‘rootward’ faces of the cell (Wisniewska et al., 2006; Scacchi et al., 2009; Zourelidou et al., 2009; Breda et al., 2017; Marhava et al., 2018) (Figs 4e, S4a). Determining whether a protein is present at both shootward and rootward faces in a cell within a contiguous file has been challenging.

To test whether Pome could be used to determine which side of the interface between two adjacent cells a protein resides, we quantified the localisation of BRXL2 and the transmembrane protein PIN2 in Arabidopsis roots. BRXL2 has been reported to localise rootward in roots (Marhava et al., 2020) and PIN2 to localise shootward in root epidermis cells (Wisniewska et al., 2006). We quantified the pixel intensity at multiple concentric ‘rings’ of the plasma membrane. Fluorescence in the proximal membrane region (within the solid rings in Fig. 4d) is contributed by the selected (target) cell, while fluorescence in the distal membrane region (within the dashed rings) is considered to be contributed by the neighbouring cell. With this modified Pome protocol, we validated BRXL2’s rootward localisation pattern in lateral root cap cells (Fig. 4e–g) and PIN2’s shootward localisation in root epidermal cells (Fig. S4). This modified version of Pome can also be applied to validate bi‐polar localisation, when polarity proteins are present at both shootward and rootward faces. In this case, no appreciable differences will be observable between proximal and distal measurements at the membrane sections shared between the continuous cell file and the signal intensity of the polarity reporter will be higher at such membrane sections. The same principle of capturing pixel intensity of a reporter across concentric ‘rings’ could also be used to determine the redistribution of proteins between membrane and cytoplasm, a common response to environmental perturbation in plants (Zourelidou et al., 2009; Marhava et al., 2018).

Plant proteins exhibit staggering variation in cortical polar domains. They can be found linked to dispersed ACDs, in contiguous cell files aligned with organ axes, or nestled in cell corners. Pome can quantify dynamic polarity in these different contexts and complements other recent advances in cell segmentation and quantitative image analysis (Wolny et al., 2020). Pome converts a once low‐throughput and qualitative procedure into a semi‐automated one that is amicable to statistical analysis. It could be even more powerful when combined with other microscopy techniques such as fluorescence resonance energy transfer (FRET) that directly measure protein interaction.

Ultimately, we expect fluorescence microscopy and tools like Pome to answer some and open new questions in cell biology. In our exploration of stomatal lineage proteins in two plant species, we were able to find that BASL, while a central hub in stomatal polarity, may be preceded by BRXL2 polarity in Arabidopsis and must be supplanted by other mechanisms for establishing polar localisation of the MAPKKK BdYDA1 in Brachypodium. Pome also allowed us to validate the rootward and shootward localisation of BRXL2 and PIN2, respectively, in Arabidopsis roots. Furthermore, the utility of Pome is not limited to plants, as we were also able to use it to quantify PAR‐2 polarity in C. elegans embryos (Hubatsch et al., 2019) (Fig. S5). The simplicity and versatility of our pipeline make it accessible to the broad research community regardless of previous programming skills.