Automated cell tracking identifies mechanically oriented cell divisions during Drosophila axis elongation

Axis elongation is a conserved morphogenetic process in which embryos extend their anterior-posterior (AP) axis. In Drosophila, axis elongation occurs in the germband, an epithelial monolayer that gives rise to the epidermis and the central nervous system (Hartenstein and Campos-Ortega, 1985). During axis elongation the germband extends more than twofold (Fig. S1) in a process mainly driven by directional cell rearrangements (Irvine and Wieschaus, 1994; Bertet et al., 2004; Zallen and Wieschaus, 2004; Blankenship et al., 2006). Cells intercalate between their dorsal or ventral neighbours, thus promoting AP tissue elongation.

The directionality of cell intercalation during germband extension is controlled by AP patterning (Irvine and Wieschaus, 1994). AP patterning establishes tissue-level planar polarity of cytoskeletal and junctional proteins (Zallen and Wieschaus, 2004; Blankenship et al., 2006; Paré et al., 2014). Actin and myosin localize preferentially to cell-cell contacts perpendicular to the AP axis, generating contractile forces that promote systematic disassembly of cell interfaces (Bertet et al., 2004; Zallen and Wieschaus, 2004; Blankenship et al., 2006; Rauzi et al., 2008; Fernandez-Gonzalez et al., 2009). At the same time, anisotropic pulsatile behaviours of germband cells and endoderm internalization in the posterior pole of the embryo produce AP-oriented deformation (strain) that causes cell elongation (Butler et al., 2009; Fernandez-Gonzalez and Zallen, 2011; Sawyer et al., 2011) and facilitates the polarized assembly of new cell-cell contacts parallel to the AP axis, thus driving tissue extension (Collinet et al., 2015; Lye et al., 2015; Yu and Fernandez-Gonzalez, 2016).

Oriented cell divisions contribute to germband extension (da Silva and Vincent, 2007). Cell divisions are predominantly parallel to the AP axis at the posterior tip of the extending germband, and inhibiting cell division slows down germband elongation. More anteriorly, lateral germband cells and mesectoderm cells also divide, forming distinct mitotic domains (Foe, 1989). Mesectoderm cells form the ventral midline, separate the ectoderm from the internalized mesoderm, and eventually form a discrete set of glia and neurons (Jacobs and Goodman, 1989; Klämbt et al., 1991). It is currently unknown if the divisions in the anterior germband are oriented during Drosophila axis elongation.

Mechanical forces can orient cell division in developing animals (Le Goff and Lecuit, 2011; Mao et al., 2011; Campinho et al., 2013; Mao et al., 2013; Bosveld et al., 2016). In the Drosophila embryo, defects in AP patterning disrupt cell division orientation on the posterior germband (da Silva and Vincent, 2007). Notably, defective AP patterning disrupts both AP-oriented and dorsal-ventral (DV)-oriented forces and cell intercalation (Irvine and Wieschaus, 1994; Zallen and Wieschaus, 2004; Blankenship et al., 2006; Fernandez-Gonzalez et al., 2009; Fernandez-Gonzalez and Zallen, 2011; Collinet et al., 2015). Thus, it is not clear whether oriented cell divisions during germband extension are cell-autonomously regulated by AP patterning or if the orientation of cell division is non-autonomously determined by the effect of AP patterning on the distribution of mechanical forces.

Investigation of cellular dynamics from microscopy images requires cell delineation and tracking. The watershed algorithm (Beucher, 1992), a region-growing method, is often used as the basis for cell segmentation from fluorescence microscopy images (Aigouy et al., 2010; Fernandez-Gonzalez and Zallen, 2011; Mashburn et al., 2012; Mosaliganti et al., 2012; Leung and Fernandez-Gonzalez, 2015). However, the success of watershed-based approaches critically depends on the identification of a single seed point within each cell to be segmented. Otherwise, segmentation errors occur and the resulting polygons need to be manually corrected in a process that is time consuming and error prone. Tracking is often accomplished by linking cells frame-to-frame based on cell overlap (Aigouy et al., 2010; Mashburn et al., 2012; Guirao et al., 2015). To further refine tracking and compensate for data with low temporal resolution, morphological features, such as cell size or shape, and topographical information, including the identity of cell neighbours, can be used (Etournay et al., 2016). However, these tracking methods depend heavily on the accuracy of the segmentation. Alternatively, cell tracking can be made segmentation independent by matching image subregions instead of individual cells. Optic flow uses the cross-correlation of two images to calculate local similarities (Raffel et al., 1998) and can be used to track cells based on matching fluorescence patterns (Mosaliganti et al., 2012; Yu and Fernandez-Gonzalez, 2016). Segmentation-independent methods can be computationally expensive when fine spatial or temporal sampling is necessary, for instance in the case of rapidly moving cells. Thus, integrating segmentation and tracking can be beneficial for the effectiveness of both approaches (Wahlby et al., 2004; Schiegg et al., 2015).

Here, we use in vivo confocal microscopy to investigate cell division dynamics in the anterior germband during Drosophila axis elongation. We develop a novel image analysis method for cell delineation and tracking, and we use machine learning to automatically identify dividing cells. We find that, in contrast to lateral germband cells, mesectoderm (ventral) cells divide parallel to the AP axis of the embryo. Oriented cell divisions increase cell density along the AP axis on the ventral midline of the embryo, where cells do not intercalate. We use laser ablation to mechanically isolate ventral cells from intercalating cells or from the influence of the AP poles of the embryo and we find that AP-oriented forces from the embryonic poles determine the direction of cell division. We propose that tension parallel to the AP axis orients cell division in the ventral germband, thus increasing AP cell density, reducing cell strain and facilitating axis elongation.

To quantify cellular dynamics from confocal microscopy images of embryos expressing a fluorescently tagged cell outline marker, we developed an algorithm integrating cell segmentation and tracking. To automatically identify one seed per cell we used adaptive thresholding to separate membrane and cytoplasmic pixels, followed by a distance transform (Fernandez-Gonzalez and Zallen, 2011; Leung and Fernandez-Gonzalez, 2015). The local maxima of the distance transform represented the cytoplasmic pixels furthest from the cell membrane and were used as seeds. In images of Drosophila embryos expressing Gap43:mCherry (Martin et al., 2010) and undergoing axis elongation, 95.7±1.2% of the seeds generated inside the embryo by our approach were correctly placed as the only seed within one cell (Fig. 1A). Errors in seed detection resulted in over- or undersegmentation of one or more cells (Fig. 1A′). Furthermore, our method also placed seeds in the background or within cells that were not completely included in the field of view. As a consequence, only 74.0±5.3% of the polygons resulting from watershed-based seed expansion represented properly segmented cells (Fig. 1C).

Manual correction of segmentation errors is time consuming. It took 202±26 s per image to correct the results of the watershed algorithm. To accelerate the correction of segmentation results, we developed tools to interactively add and remove seeds before watershed segmentation. When we edited seeds the segmentation results improved significantly, and 94.6±0.5% of cells were correctly segmented (P=1.1×10⁻³), with the remaining errors corresponding to cells that were not completely within the field of view (Fig. 1B-C). Seed editing only required 66±11 s per image, significantly faster than polygon editing (P=1.2×10⁻⁴; Fig. 1D). Our results show that seed editing is an efficient method to minimize errors in watershed-based cell segmentation.

In spite of the improvement over polygon editing, a significant amount of time is necessary for seed editing in time-lapse sequences consisting of multiple images. To reduce the time necessary to segment time-lapse images, we transferred edited seeds from one time point to the next. The propagation of seeds in time also implicitly tracks the cells (Pinidiyaarachchi and Wählby, 2005). We tested this approach by segmenting cells expressing Gap43:mCherry in Drosophila embryos imaged every 15 s during germband extension. Copying seeds led to segmentation errors as a consequence of cell movement (Fig. 1E,F, arrowheads). The percentage of correctly segmented cells declined from 98.8±0.9% at the first time point, after seed editing, to 42.5±2.1% for images acquired 5 min later (P=7.2×10⁻⁹; Fig. 1I). On average, apical cell areas do not change significantly during germband extension before cell division (Fernandez-Gonzalez and Zallen, 2011). The segmentation errors caused by seed copying were further demonstrated by a significant increase in the range of cell areas measured from the segmented images: the standard deviation of the distribution was 19.1±1.6 μm² initially (stage 7 of embryonic development) versus 37.0±2.2 µm² after 5 min (P=1.9×10⁻⁴; Fig. 1J,K). Together, our data indicate that seed copying increases the number of segmentation errors.

To compensate for cellular movements when transferring seeds across images, we used the optic flow to estimate cell displacements. We divided each pair of consecutive images into 17.1×17.1 μm² windows (∼2×2 cell diameters) and calculated the spatial cross-correlation between the pixel values in corresponding windows. The cross-correlation maximum indicates the displacement of the signal. We obtained one vector per window, and the resulting vector field was interpolated at the positions of the seeds in the initial time point. Seeds were translated by the corresponding vector before transferring to the next time point. Using optic flow to transfer seeds led to significantly more cells correctly segmented after 5 min (89.7±4.9%, P=2.1×10⁻⁵) and a lower standard deviation of the measured areas (24.9±3.2 µm², P=1.4×10⁻²; Fig. 1G,I-K), demonstrating that seed propagation using optic flow preserves segmentation quality.

To further refine the segmentation results, we integrated seed detection and watershed-based expansion. The seeds for the first image were grown using the watershed algorithm. Seeds that were closer than 0.8 μm to their enclosing, watershed-generated polygon were translated to the geometric centre of the polygon before propagation to the next time point using optic flow (Fig. 1H, white arrows). Using this approach, 94.9±1.6% of cells were correctly segmented 5 min after the initial time point (Fig. 1I), and the standard deviation of the measured cell area did not increase significantly over time (23.6±2.5 µm², P=0.17; Fig. 1J,K). Thus, integration of watershed-based seed expansion and seed propagation using optic flow improved segmentation accuracy by over 120% with respect to seed copying, and minimized the user interactions necessary to delineate and track cells from confocal microscopy movies.

During embryonic development, cells not only move but also divide. We extended our algorithm to detect dividing cells and split their seeds before propagating to the next time point. To determine when a cell divided, we quantified changes in cell morphology (Fig. 2A) using features that ensured that cells were only classified as dividing immediately before their division was complete (Movie 1), which was crucial for proper seed splitting and segmentation. We measured the maximum change in cell area as the ratio between the current area and the minimum recorded area for a cell. Dividing cells increased their apical area by 106±15% (Fig. 2B), whereas the maximum area increase of non-dividing cells during the same time was 42±4% (P=8.6×10⁻⁵; Fig. 2E). The shape factor (Cox, 1927), which is proportional to the ratio of perimeter² to area (1 for circles, greater than 1 for other shapes), decreased towards 1 as cells rounded up, and then increased rapidly when the cytokinetic furrow formed (Fig. 2C). On average, the minimum recorded shape factor was 1.30±0.01 for dividing cells and 1.37±0.01 for non-dividing cells (P=7.7×10⁻⁶; Fig. 2F). We quantified the characteristic dumbbell shape of dividing cells during cytokinesis by calculating the distance between the cell centroid and each point in the polygon resulting from the cell segmentation, and measuring the ratios between each of the two local distance minima (corresponding to the cleavage furrow) and the maximum (corresponding to the distance to one of the cell poles, Fig. 2D). The ratios increased towards 1 as the cells rounded up in preparation for division, and they decreased rapidly as the cleavage furrow formed (Fig. 2D′). Both ratios were significantly smaller for dividing cells with respect to non-dividing cells (0.36±0.01 versus 0.41±0.01 for the deeper end of the furrow, P=5.3×10⁻⁵; and 0.42±0.01 versus 0.49±0.01 for the shallower end, P=7.5×10⁻⁷; Fig. 2G,H). Finally, the distance between the cell centroid and the segmented polygon displayed a strong periodic pattern immediately before division, with two periods within the perimeter of the cell corresponding to the two daughter cells (Fig. 2I). Thus, we used the first ten integer frequency components of the Fourier transform of the centroid-to-polygon distance as ten additional features to distinguish between dividing and non-dividing cells (Fig. 2J). For a frequency of 2, representing the presence of two peaks and two troughs in the distance plot, the magnitude of the Fourier transform was 2.2-fold greater for dividing cells (P=8.4×10⁻³⁸; Fig. 2J), demonstrating the presence of two clearly defined lobes before cell division.

We applied a statistical method, logistic regression, to detect dividing cells using the 14 measured features (Fig. 2E-H,J) and a training set of cells. Each cell in the training set was represented in 15-dimensional space, where 14 dimensions corresponded to the measured features, and the dependent variable was the cell classification as dividing (1) or non-dividing (0). A probability function, h, was defined by fitting a logistic function (see Materials and Methods) to the distribution of cells in 15-dimensional space. The value of h for a given set of features determines the probability that a cell with those features is dividing. Cells with a probability greater than 0.5 were considered to be dividing. We split the seed corresponding to a dividing cell into two new seeds that were placed on the longest axis of the cell, at 50% of the distance between the cell centroid and the cell boundary. To validate our approach, we determined the accuracy of classification for a test set of cells (formed by 30 dividing and 60 non-dividing cells in seven embryos and independent from the training set) using training sets of different sizes, all with a 1:1 ratio of dividing and non-dividing cells (Fig. 2K). Using a training set including 52 cells, we correctly classified over 90% of the cells in the test set, with 2% of non-dividing cells classified as dividing (false positives). Using a training set with 80 cells, we correctly classified 97% of the test cells, with 3% false positives (Fig. 2K). Therefore, our method can efficiently detect and track dividing cells (Movie 1), thus allowing quantification of features including cell cycle duration, division orientation or morphological and molecular (a)symmetries.

To illustrate the generality of our method, we used it to segment and detect a different cell type, namely the ingressing neuroblasts of the early embryo. As neuroblasts ingress, their apical area decreases and their circularity increases (Movie 2, Fig. S2A). We quantified the change in area for a cell as the ratio between the current area and the first recorded area. Neuroblasts displayed lower area change and minimum shape factor values than non-ingressing cells (0.23±0.02 versus 1.19±0.07 for area change, P=2.2×10⁻¹⁴; and 1.21±0.01 versus 1.43±0.02 for minimum shape factor, P=8.3×10⁻¹²; Fig. S2B). Consistent with their roundness, the ratios of minimum to maximum distance from the centroid to the cell boundary were both greater for neuroblasts (0.48±0.02 versus 0.39±0.02 for min₁/max, P=4.1×10⁻³; and 0.55±0.02 versus 0.45±0.02 for min₂/max, P=7.3×10⁻⁴; Fig. S2C). Ingressing neuroblasts displayed lower amplitudes in the frequency components of the Fourier transform of their centroid-to-polygon distance (Fig. S2D). Using a training set formed by up to 15 neuroblasts and 15 non-ingressing cells, we correctly classified over 90% of ingressing neuroblasts in a test set formed by 15 neuroblasts and 15 non-ingressing cells in five embryos (Fig. S2E). Notably, removing frequency components 3-10 from the feature set resulted in 100% classification accuracy for neuroblasts and non-ingressing cells with only 12 training cells (Fig. S2E, inset). Together, these results demonstrate that, given an appropriate training set, our classification framework is able to identify different cell types from confocal microscopy movies.

Mesectoderm (ventral) and lateral cells in the anterior germband divide during axis elongation (Movie 3). To investigate if the divisions of ventral and lateral cells contribute to axis elongation, we used the tools that we developed to quantify cell division orientation. We imaged stage 7-8 Drosophila embryos expressing Gap43:mCherry to outline cells (Fig. 3A-B′). The average division orientation with respect to the AP axis for ventral cells was 24.8±2.6°, and the median was 14.0° (Fig. 3C). 55.2±7.4% of the ventral divisions occurred within 15° of the AP axis, and 84.3±4.0% of cells divided at less than 45° relative to the AP axis. To validate our automated analysis, we manually measured the angles of division for a subset of cells. We found no significant differences between automated and manual analyses (Fig. 3D). Altogether, our data indicate that ventral cells divide parallel to the AP axis of the embryo during germband extension.

Using light-sheet microscopy, we found that the onset of lateral cell divisions occurred at approximately the same time as that of ventral divisions (Movie 4). In contrast to ventral cells, the distribution of division angles for lateral cells was uniform (Fig. 3B,E). The average angle of lateral cell division was 43.4±1.7°, a significantly greater angle than that of ventral cell division (P=2.2×10⁻⁸). The median angle of lateral cell division was 42.1°. 18.1±3.0% of the cells divided within 15° of the AP axis, and 51.9±5.0% divided within 45° (Fig. 3E), both significantly lower percentages than for ventral cells (P=1.5×10⁻⁴ and 8.0×10⁻⁵, respectively). Our results show that lateral cells do not divide directionally, suggesting that the mechanisms that orient cell division in the ventral midline are spatially regulated.

Cell division angle is strongly correlated with cell shape orientation (Hertwig, 1884). To quantify cell orientation during division, we used least-squares to fit an ellipse to the polygon produced by our segmentation (Fitzgibbon et al., 1999) (Fig. 4A). We defined cell orientation as the angle of the longest axis of the ellipse relative to the AP axis. As expected, cell orientation immediately before division was closely correlated with the orientation of cell division for both ventral and lateral cells (r=0.99, P=1.3×10⁻⁵³ for ventral cells; r=0.98, P=2.4×10⁻⁶⁹ for lateral cells; Fig. 4D), thus validating our metric of cell orientation. When we examined the absolute difference between cell orientation and cell division angle we found that, between 300 s and 90 s before division, ventral cell orientation deviated more significantly from the final division angle than lateral cell orientation (P=3.5×10⁻⁴; Fig. 4B,C,E). The total angular change in cell orientation, resulting from integrating the absolute value of the major cell axis rotation over the 5 min before division, was 120.9±9.9° for ventral cells, significantly greater than the 84.1±4.7° of lateral cells (P=1.2×10⁻³; Fig. 4F). These data show that ventral cells change their alignment more significantly than lateral cells in preparation for division, suggesting that ventral cells might be responding to directional cues that determine the orientation of division.

Lateral germband cells intercalate and thus relieve AP strain (Collinet et al., 2015; Lye et al., 2015). Conversely, ventral cells did not intercalate during germband extension (Movie 5). As a consequence, we predicted that ventral cells sustained greater AP strain (deformation) during germband extension than lateral cells. We measured strain as the percentage change in AP or DV length between 10 and 5 min before the first ventral division (Fig. 5A-C). Ventral cells sustained tensile AP strain and significantly lower compressive DV strain (7.5±1.3% versus −3.3±1.9%, respectively, P=8.1×10⁻⁶; Fig. 5D). The AP strain sustained by ventral cells was greater than that of lateral cells (1.3±2.1%, P=1.3×10⁻²), which displayed compressive strain along the DV axis (−8.2±1.9%) (Fig. 5D). Thus, 5 min before the onset of cell division, ventral and lateral cells sustain different types of deformation.

Oriented cell divisions could alleviate AP strain in ventral cells by reducing their AP length. Before their respective divisions, ventral cells were significantly longer along the AP axis than lateral cells (11.1±0.3 µm versus 7.8±0.4 µm 600 s before division, P=6.6×10⁻⁸; and 12.2±0.2 µm versus 10.0±0.2 µm 300 s before division, P=2.7×10⁻⁷; Fig. 5E-G). Cell division led to a significant reduction of AP length for ventral but not lateral cells [9.8±0.1 µm immediately after division for both ventral cells (P=2.6×10⁻¹⁴) and lateral cells (P=0.35); Fig. 5G]. The reduction in AP length was associated with increased cell density along the AP axis. We measured cell density for both ventral and lateral cells, 5 min before and 12 min after division, by calculating the average number of cells intersected by three 80 μm lines parallel to the AP axis and ∼7 μm (one cell diameter) apart (Fig. 5H,I). Ventral AP cell density increased significantly after oriented cell divisions, from 143.3±5.4 cells/mm to 196.7±1.6 cells/mm (P=3.1×10⁻⁴; Fig. 5J). By contrast, lateral AP cell density did not increase after cell divisions, but rather decreased from 252.5±5.7 cells/mm to 218.3±13.6 cells/mm (P=0.05; Fig. 5J). The lateral and ventral AP cell densities after division were not significantly different from each other (P=0.19). Together, our data show that ventral cells sustain greater AP strain than lateral cells during germband extension, and that oriented cell divisions selectively reduce the AP length of ventral cells, suggesting that oriented cell divisions in the mesectoderm might alleviate cell strain.

To further investigate whether ventral cell divisions alleviate AP strain, we injected embryos with dsRNA against string (stg) (Movie 6). String, a Cdc25 homologue (Edgar et al., 1994), is required for post-blastoderm mitoses in Drosophila embryos. We found that the AP length of ventral cells at the end of germband extension was significantly greater in embryos depleted of String than in controls (13.7±0.5 µm versus 8.7±0.3 µm, respectively, P=6.3×10⁻¹⁴; Fig. 6A-C). The AP length of ventral cells in stg dsRNA embryos did not exceed the AP length of ventral cells before division in control embryos (12.9±0.4 µm, Fig. 6A-C). In controls, and especially in stg dsRNA embryos, myosin localized to cell interfaces parallel to the AP axis within the mesectoderm and at the boundaries between mesectoderm and ectoderm (Fig. 6A′,B′), suggesting that myosin might resist excessive AP-oriented deformation.

To investigate how ventral cell divisions might contribute to axis elongation, we compared the apical area of cell duplets resulting from ventral divisions in control embryos with the maximum area of ventral cells in stg dsRNA embryos. The area of the duplets was significantly greater (83.0±3.5 µm² versus 68.6±2.3 µm² for single ventral cells in stg dsRNA, P=9.0×10⁻⁴; Fig. 6D). Together, these results suggest that ventral divisions increase the surface area of the mesectoderm, a tissue that does not intercalate, in a process that may contribute to axis elongation.

Mechanical forces parallel to the AP axis of the embryo contribute to germband extension (Irvine and Wieschaus, 1994; Collinet et al., 2015; Lye et al., 2015; Yu and Fernandez-Gonzalez, 2016). To investigate the role of forces in cell division alignment during Drosophila axis elongation, we used laser ablation to mechanically isolate ventral cells from tension generated by the internalization of the endoderm or by intercalating cells. To decouple ventral cells from the embryonic poles, we created two incisions across the ventral midline and parallel to the DV axis in stage 7 embryos, prior to the first ventral division (Fig. 7C). We quantified cell division orientation relative to the AP axis for ventral cells between the two incisions (Fig. 7D,E). In sham-irradiated controls, ventral divisions were oriented parallel to the ventral midline, with a mean angle of 23.5±2.4° and a median of 15.3°. When ventral cells were decoupled from the anterior and posterior ends of the embryo, ventral divisions displayed a mean orientation of 39.8±4.1°, significantly greater than in controls (P=1.0×10⁻³), and a median of 30.7°. The distribution of cell division orientations was significantly more uniform when cells were isolated from forces from the anterior and posterior ends of the embryo (Fig. 7D; P=8.8×10⁻³). By contrast, when we isolated ventral cells from intercalating cells by creating an incision lateral to the ventral cells and parallel to the AP axis (Fig. 7B), ventral divisions were still oriented along the AP axis, with a mean angle of 21.6±3.1° and a median of 18.0° (Fig. 7D,E). Together, our data indicate that forces from the embryonic poles, but not directly transmitted from intercalating cells, orient ventral cell divisions during Drosophila axis elongation.

The mechanisms that orient cellular behaviours during embryonic development remain unclear. We introduce novel quantitative imaging tools to investigate the orientation and dynamics of cell division. We find that ventral but not lateral germband cells undergo oriented cell divisions during axis elongation. Oriented cell divisions increase cell density parallel to the AP axis of the embryo, alleviate AP strain, and may facilitate tissue elongation by increasing the surface area of the mesectoderm. Using laser ablation, we find that isolating ventral cells from the mechanical influence of the anterior and posterior ends of the embryo significantly alters the orientation of divisions, suggesting that tissue-wide forces determine cell division orientation during Drosophila axis elongation.

To investigate oriented cell divisions during germband extension, we have developed image-based cell segmentation and classification tools based on the watershed algorithm. Our method provides several advantages over previous approaches. First, we allow the user to correct seeds, instead of polygons, which minimizes user interactions (Mashburn et al., 2012). Second, corrected seeds can be transferred to other images in time-lapse sequences while taking cell movements into account by using optical flow and integrating seed propagation with cell segmentation. Thus, seeds need only be edited in one image, further reducing user intervention. Third, we apply a statistical method, logistic regression, to determine the probability that a cell is dividing based on cell morphology. Using logistic regression and a relatively modest training set of 52 cells, we correctly classify over 90% of cells in a test set, with a false-positive rate of only 2%. We provide interactive tools to correct the results of logistic regression, and we use the corrections to further train our algorithm, thus seamlessly integrating user knowledge into our automated classification scheme. Importantly, the use of machine learning confers generality to our approach, as creating different training sets allows application of the same method to other cell types, tissues and/or fluorescent markers.

Our data suggest that mechanical cues orient cell division during germband extension. Endoderm internalization on the posterior end of the embryo imposes AP-oriented tension on the germband (Collinet et al., 2015; Lye et al., 2015) that could orient cell divisions. It has been proposed that segmental patterning orients cell division in the posterior germband (da Silva and Vincent, 2007). In embryos maternally triple mutant for bicoid, nanos and torso-like, which completely lack AP patterning, all posterior divisions during germband extension are randomly oriented (da Silva and Vincent, 2007). However, torso-like is necessary for endoderm invagination (Degelmann et al., 1986), and therefore the orientation of posterior-ventral divisions may be regulated by global mechanical cues generated as the endoderm is internalized.

We find that on the anterior end of the germband, ventral, but not lateral, cells undergo oriented division. The curvature of the Drosophila embryo is greater on the ventral than on the dorsal or lateral surfaces (He et al., 2010). Thus, as the endoderm is internalized and the germband elongates, ventral cells need to cover a greater surface area than lateral cells. In addition, lateral cells intercalate during axis elongation, thus increasing cell density along the AP axis and partially relieving the tension caused by the internalization of the endoderm (Collinet et al., 2015; Lye et al., 2015). By contrast, ventral cells do not intercalate, and they sustain increased AP strain with respect to lateral cells before the onset of division. Together, our data support a model in which ventral cells divide directionally to alleviate the tension caused by endoderm invagination, increased ventral curvature and the absence of intercalary behaviours.

The mechanisms by which physical forces orient cell division during Drosophila axis elongation remain unclear. In Drosophila neuroblasts, the asymmetric localization of the polarity factor Par-3 (Bazooka) determines the direction of division (Schober et al., 1999; Wodarz et al., 1999). Par-3 is planar polarized in lateral germband cells (Zallen and Wieschaus, 2004; Blankenship et al., 2006), which do not display a bias in the directionality of their division, suggesting that Par-3 might not be involved in cell division orientation during germband extension. Par-3 regulates cell division orientation by recruiting the G-protein regulator Pins (Schober et al., 1999; Wodarz et al., 1999; Yu et al., 2000; Schaefer et al., 2001) and the Pins-binding protein Mud (Bowman et al., 2006; Izumi et al., 2006; Siller et al., 2006), which form a complex that interacts with the microtubule-based motor Dynein and facilitates spindle orientation (Merdes et al., 1996). Recent data show that in the dorsal thorax of the Drosophila pupa, Mud localizes to tricellular junctions independently of Pins and regulates the pulling forces that astral microtubules exert on centrosomes (Bosveld et al., 2016). Thus, the distribution of tricellular junctions around a dividing cell determines centrosome position, spindle alignment and cell division orientation. Investigating the distribution of tricellular junctions around ventral cells and how the different cell behaviours and forces at play in the germband affect tricellular junctions might therefore be crucial to understand how mechanical forces direct cell division orientation during Drosophila axis elongation.

For live imaging we used stage 7-8 embryos expressing sqh-gap43:mCherry (Martin et al., 2010) and sqh-sqh:GFP (Royou et al., 2004).

Drosophila embryos were dechorionated for 2 min using a 50% bleach solution in water. Embryos were mounted in halocarbon oil 27 (Sigma-Aldrich) between an 18×18 mm coverglass and an oxygen-permeable membrane (YSI). Embryos were imaged using a Revolution XD spinning disk confocal microscope with an iXon Ultra 897 camera (Andor) and either a 40× (NA 1.35) or 60× (NA 1.35) oil-immersion lens (Olympus). z-stacks consisting of 14 slices 0.3 μm apart were acquired every 15 s at 16 bits. One to four slices were projected per stack.

For light-sheet microscopy, embryos were mounted in warm 2% agar inside a glass capillary and the agar allowed to set. Embryos were extruded from the capillary and mounted in the water-filled chamber of the light-sheet microscope. Dual-sided light-sheet excitation was provided by two 20× long-working-distance air objectives (Olympus), and emission was imaged through a 20× (NA 0.5) water-immersion objective (Olympus). Ventral and lateral z-stacks consisting of 14 slices 3 μm apart were acquired every 25 s using a Neo sCMOS camera (Andor). Three slices were projected per stack.

To delineate and track dividing cells from fluorescence microscopy movies, we developed a new method based on the watershed algorithm for cell segmentation, optic flow for seed propagation, and machine learning for division detection. Our method was implemented using MATLAB (MathWorks) and the DIPimage toolbox (TU Delft, The Netherlands; http://www.diplib.org/dipimage), and integrated into SIESTA (Fernandez-Gonzalez and Zallen, 2011), an image analysis platform that we have developed (available at http://individual.utoronto.ca/quantmorph).

The watershed algorithm is a region-growing segmentation method based on the identification and expansion of one seed point per cell (Beucher, 1992). We identified seeds exclusively for the first time point of an image sequence using an adaptive threshold (Fernandez-Gonzalez and Zallen, 2011). Seeds were edited using interactive tools provided by SIESTA (Leung and Fernandez-Gonzalez, 2015). Seeds were then propagated to subsequent time points in the image sequence using optic flow.

The optic flow is a vector field that quantifies local signal displacements across two images. To propagate watershed seeds, we took pixels (one in every 32) with corresponding coordinates in the source and target images, and defined a 64×64 pixel window (approximately two cell diameters) around each pixel. We calculated the cross-correlation of the pixel values for corresponding windows in the source and target images. The maxima of the cross-correlation indicate the coordinates of a vector representing the signal displacement. The vector field was bilinearly interpolated at the positions of the seeds on the source image to obtain the optic flow at the seed points. Seeds were translated by the magnitude and direction of the corresponding vectors before transferring to the target image.

In embryos, cells do not only experience translations, but also deformations. Therefore, optic flow alone did not always successfully propagate seeds. To address this issue, we integrated seed propagation and cell segmentation. After propagating the seeds to the next time point, the watershed algorithm was used to detect cell outlines. Seeds that were within three pixels from the cell boundary were shifted to the cell centroid before propagating to the next time point. Cell tracking was implicitly performed by the seed propagation algorithm except in the case of dividing cells.

Images were rotated so that the ventral midline of the embryo was parallel to the horizontal axis. The percentage of cells correctly segmented was calculated by counting the number of cells correctly outlined and dividing by the total number of polygons resulting from the segmentation. The orientation of cell division was measured at the first time point in which the seeds were split, as the angle between a line connecting the centroids of the two daughter cells and the horizontal axis of the image. AP or DV cell length was measured as the width or the height, respectively, of a bounding box containing the cell, effectively representing the length of the cell projected on the AP or DV axis.

The stg dsRNA template was amplified by PCR from Drosophila genomic DNA using the following primer pairs with the T7 promoter sequence (5′-TAATACGACTCACTATAGGGAGACCAC-3′) added to the 5′ ends: stg T7-forward, 5′-CGGCTACAAGGAGTTCTTCG-3′; stg T7-reverse, 5′-CGTCGTGTGCGAGAAACTTA-3′. We generated dsRNA from the PCR products using the MEGAscript T7 Transcription Kit (Fisher).

sqh-gap43:mCherry;sqh-sqh:GFP embryos collected for 50-60 min were dechorionated, glued on a glass coverslip, dehydrated for 10-15 min, and covered in halocarbon oil 27. Embryos were immediately injected laterally with 1.86 μg/μl dsRNA against stg using a Transferman NK2 micromanipulator (Eppendorf) and a PV820 microinjector (WPI). Control embryos were injected with water. Embryos were incubated in a humidified chamber for 2 h at room temperature after injection. z-stacks consisting of ten slices 0.3 μm apart were acquired every 30 s at 16 bits. One to four slices were projected per stack.

To mechanically isolate cells from AP-oriented forces, we used a pulsed Micropoint N₂ laser (Andor) tuned to 365 nm to cut lines on the germband. The laser delivered 2-6 ns pulses at a power of 120 μJ per pulse at the source. We induced line wounds by a series of discrete point ablations ∼1.7 μm apart. Three to five laser pulses were delivered to each point. DV lines were 50-60 μm in length and were 80-90 μm apart along the AP axis. AP lines were 50-60 μm in length and were at least two cell layers away from the ventral midline. Line ablations were performed before completion of the first ventral division. For control experiments, the laser was fully attenuated using a neutral density filter.

We compared sample variances using the F-test. We used Student's t-test modified for samples with equal or unequal variances (based on the F-test results) to compare sample means. When three or more samples were considered, we applied Holm's correction to Student's t-test (Glantz, 2002). We used the Kolmogorov–Smirnov test to compare sample distributions. We calculated the significance of correlation coefficients by transforming the correlation value into a t-statistic using the corrcoef MATLAB function. Error bars represent s.e.m. unless otherwise indicated.

We are grateful to Anna Kobb, Teresa Zulueta-Coarasa, Jessica Yu and Hester van Dorst for comments on the manuscript; and to Ulli Tepass and Penney Gilbert for useful discussions. FlyBase provided important information for this study.