Oscillatory behaviors and hierarchical assembly of contractile structures in intercalating cells.

2.1. Markers and mutants For live imaging, we used the following markers spider:GFP (gift of Alain Debec), sqh-sqh:GFP ( Royou et al 2004 ), sqh-sqh:mCherry ( Martin et al 2009 ), ubi-E-cadherin:GFP ( Oda and Tsukita 2001 ) and sqh-GFP:moesin ( Kiehart et al 2000 ). Mutants were halo Df(2L)dpp[s7−dp35] snail IIG05 ; sqh-sqh:GFP (gift from Adam Martin) and the progeny of ubi-Ecadherin:GFP; bcd E1 nos L7 tsl 146 females. 2.2.

Time-lapse imaging

Embryos were collected for 1 h, dechorionated in 50% bleach, transferred to a drop of halocarbon oil 27 (Sigma) on a cover glass, and mounted on an oxygen-permeable membrane (YSI). GFP was excited with an Argon line (488 nm, 100mW, Melles Griot). mCherry was excited with a Krypton laser (568 nm, 1 mW, Melles Griot). A 63× oil immersion lens (Zeiss, N.A. 1.4) on an UltraView RS spinning disk system (Perkin Elmer) was used for imaging, except in figures 6(A) and (B) where a 40× oil immersion lens (Zeiss, N.A. 1.3) was used. 16 bit, 2-color Z -stacks were acquired at 0.5 μ m steps every 15 s and projected for analysis (15 slices per stack). 2.3.

Injections

Embryos from 30–60 min collections were dechorionated for 2 min in 50% bleach, lined up on an agarose pad, transferred to a stripe of heptane glue on a cover glass, dehydrated for 7 min, and covered in 1:1 halocarbon oil 27:700. For α -catenin knockdown, double-stranded RNA against α -catenin was injected ventrally in syncytial embryos (stage 3) at 2 μ g μ l −1 . Templates to produce double-stranded RNA were generated by PCR from genomic DNA with the following primer pairs, containing the T7 promoter sequence (5′-TAATACGACTCACTATAGGGAGACCAC-3′) at the 5 end: α -catenin T7-forward 5′-ATGAGTCAAAAAGATAACAGCCCAG-3′ α -catenin T7-reverse 5′-CTTGATCTCGTAGAACTTTGACTGC-3′. Embryos were incubated in a humidified chamber at 25 °C and imaged at stages 7 or 8. For myosin knockdown, Rho-kinase inhibitor (Y-27632 dihydrochloride, Tocris Bioscience, 100 mM) was injected ventrally into the perivitelline space of stage 7 or stage 8 embryos and imaged immediately ( Fernandez-Gonzalez et al 2009 ). Injected solutions are predicted to be diluted 50-fold in the embryo. 2.4. Cell segmentation, tracking and quantification Algorithms described in this section were developed in Matlab (Mathworks) and DIPImage (TU Delft), and integrated in SIESTA. To identify the outlines of cells expressing E-cadherin:GFP, we implemented a fully automated approach based on the watershed algorithm ( figure 1(A) ). We used an adaptive threshold to identify medial versus junctional pixels in 16 bit projections of the original Z -stacks. The threshold value was the mean pixel value of a 30 × 30 pixel window around each pixel ( MacAulay and Palcic 1988 ). A distance transform was applied to the resulting binary image to compute the distance from medial pixels to the closest cell interface. The local maxima of the distance transform (pixels at least 0.24 μ m away from edges) were selected as seeds. Seed size, shape, and position were used to identify exactly one seed per cell. Seeds were expanded on a Gaussian-smoothed version of the projected image (Gaussian width was 0.13 μ m) using the watershed algorithm ( Beucher 1992 ). When manual correction was necessary, it was generally at the level of the seeds, which were rapidly edited with the annotation tools provided by SIESTA. Sqh:GFP and GFP:Moe have a nonuniform distribution and a strong medial component. Therefore, automated segmentation of these signals required extensive manual correction. In addition, when junctional integrity was lost, cells detached from their neighbors, impeding the automated detection of cell boundaries. For these reasons, we developed a semi-automated segmentation strategy based on the LiveWire algorithm ( Mortensen et al 1992 ). The user moves the mouse around the cell outline and the brightest path between consecutive points is automatically identified and displayed on the image ( movie S1 available at stacks.iop.org/PhysBio/8/045005/mmedia ). This path is updated in real time as the user moves the cursor, allowing immediate correction of segmentation errors. In the LiveWire implementation described here, a 16 bit projection of the original Z -stack was cropped around the initial and the current positions of the cursor to increase computational speed and allow real-time user interaction. The cropped image was inverted so that cell edges were dark and medial regions were bright. A weighted graph was built based on the inverted image, with one node per pixel, and bidirectional connections between each pixel and its eight immediate neighbors. Connections were weighted by the pixel value corresponding to the end node, such that it was ‘lighter’ to move toward dark pixels (cell edges) and ‘heavier’ to move toward bright pixels (medial regions). Finally, Dijkstra’s minimal cost path extraction algorithm ( Dijkstra 1959 ) was used to calculate the ‘lightest’ path between the nodes representing the initial and the current cursor positions, and this path was displayed on the original, uncropped image. Cells were tracked over time using a maximum-proximity algorithm based on the position of their corresponding watershed seeds. Because intercalating cells in the germband do not dramatically change position within 15 s, the maximum interval in our time-lapse sequences, cell tracking was done simply by projecting each seed onto the next time point and identifying the closest neighbor. In rare cases in which two seeds mapped onto the same seed in the following time point, the user was asked to identify the correct connections. The length of a cell along the AP and DV axes was calculated in two ways. In one method we superimposed on the cell outline an array of lines 1 pixel (0.2 μ m) apart and parallel to the axis in question ( figure 1(B) ). Cell length was defined as the mean length of the intersecting segments. In the second method, the cell outline was fitted with an ellipse ( Fitzgibbon et al 1999 ). The resulting ellipse was shifted until it was centered at the coordinate origin, and the intersection points with the AP and DV axes were used to determine the length of the cell along those two axes. Both methods produced similar results. Here we show results obtained using the first method. To quantify junctional and medial protein levels, each cell was divided into two compartments. The junctional compartment was determined by a 3-pixel-wide (0.6 μ m) dilation of the cell outline identified using watershed or LiveWire segmentation. The medial compartment was obtained by inverting a binary image representing the junctional compartment. Protein concentrations were quantified as the mean pixel value in each compartment. Changes in cell area and protein concentration were defined as (1) Δ area ( t ) = area ( t ) − area ( t − 60 s ) (2) Δ protein ( t ) = protein ( t ) − protein ( t − 60 s ) When necessary, the effect of photobleaching was corrected by dividing the results at each time point by the mean pixel value in the entire image. 2.5. Laser ablation An N 2 Micropoint laser (Photonic Instruments) tuned to 365 nm was used to ablate junctional and medial cell domains using ubi-E-cadherin:GFP to guide the ablations. The laser delivers 2–6 ns, 120 μ J pulses, producing wounds ~1 μ m in diameter. Cells outside the site of ablation were not damaged under our experimental conditions (10 pulses, 50% attenuation). Laser ablation induces local relaxation of mechanical tension, displacing nearby cell vertices. The initial velocity of displacement can be used to quantify the tension released ( Hutson et al 2003 , Fernandez-Gonzalez et al 2009 ), under the assumption that local viscoelastic properties are homogeneous throughout the tissue. Cell outlines were automatically segmented using SIESTA. The positions of cell vertices were extracted by scanning a 3×3 pixel kernel across the segmented image to detect small regions where three or more cells met. Cell vertices were tracked over time using a maximum proximity algorithm after subtraction of the average vertex movement in each time point. The peak radial velocity of displacement of vertices within 6 μ m of the ablation site was used to measure the local relaxation of forces. The directionality of force propagation was assessed by measuring the peak velocity of vertex displacement according to vertex position with respect to the AP axis. 2.6.

Monte Carlo simulations

At each time point, cells were classified as contracting or expanding based on tracking of their apical area. The spatial pattern of contracting and expanding cells at time t was quantified as the average fraction of neighbors of a contracting cell that are also contracting: (3) contracting_neighbors ( t ) = 1 N C ∑ i = 1 N C n i C n i where N C is the number of cells that are contracting their apex at time t , i indexes over all those cells, n ic is the number of neighbors of cell i that are also contracting, and n i is the total number of neighbors of cell i . Two types of Monte Carlo simulations were carried out, obtaining similar results. In one case, the temporal sequences of cell area values were randomized between cells, such that cells oscillate independently while maintaining the in vivo period of oscillation (not shown). In a second approach, cells were randomly reassigned as contracting or expanding at each time point based on the frequencies observed in vivo . This is equivalent to assuming that the period of oscillation is random and that the cells oscillate independently from their neighbors. 2000 simulations were run for each image analyzed. 2.7.

Statistical analysis

Sample variances were compared using the F -test ( Glantz 2002 ). Sample means were contrasted using Student’s t- test, applying Holm’s correction when three or more groups were considered. The significance of correlation coefficients was evaluated by transforming the correlation value into a t statistic using the Matlab function corrcoef (Mathworks). The Kolmogorov–Smirnov test was used to compare sample distributions. Errors indicate the standard error of the mean unless otherwise noted. P < 0.05 was used to determine significant differences. To determine the probability of erroneously reporting no correlation between cell area and medial myosin II changes, we randomly selected n cells in figure 4(K) and computed the average significance of the correlation between the cell area and medial myosin II for those n cells. This process was repeated 1000 times (trials) for each value of n tested. For each value of n , the probability of erroneously reporting no correlation was the ratio between the number of trials in which the significance was P > 0.05 and the total number of trials.

3.8.

Using quantitative imaging methods to analyze cell behavior

Automated image analysis makes it possible to analyze large numbers of cells, but the statistical advantage of this approach has not been systematically compared to smaller-scale measurements. To determine the minimum sample size needed to identify the correlation between medial myosin II and decreasing apical cell area ( figure 4(K) , n = 401 cells in 6 embryos), we calculated the probability of erroneously reporting no correlation when subsets of cells were randomly selected from our data set. A sample size of 110 cells or greater was required to reduce the probability of reporting no correlation to below 0.05 ( figure 4(O) ). This example provides a framework for considering the sample sizes necessary to discern specific behaviors associated with contractile networks in the presence of heterogeneity.

Supplementary Material 1 2 3 4 5 6 7