Statistical Validation Verifies That Enantiomorphic States of Chiral Cells Are Determinant Dictating the Left- or Right-Handed Direction of the Hindgut Rotation in Drosophila

In the left–right (LR) asymmetric development of invertebrates, cell chirality is crucial. A left- or right-handed cell structure directs morphogenesis with corresponding LR-asymmetry. In Drosophila, cell chirality is thought to drive the LR-asymmetric development of the embryonic hindgut and other organs. This hypothesis is supported only by an apparent concordance between the LR-directionality of cell chirality and hindgut rotation and by computer simulations that connect the two events. In this article, we mathematically evaluated the causal relationship between the chirality of the hindgut epithelial cells and the LR-direction of hindgut rotation. Our logistic model, drawn from several Drosophila genotypes, significantly explained the correlation between the enantiomorphic (sinistral or dextral) state of chiral cells and the LR-directionality of hindgut rotation—even in individual live mutant embryos with stochastically determined cell chirality and randomized hindgut rotation, suggesting that the mechanism by which cell chirality forms is irrelevant to the direction of hindgut rotation. Thus, our analysis showed that cell chirality, which forms before hindgut rotation, is both sufficient and required for the subsequent rotation, validating the hypothesis that cell chirality causally defines the LR-directionality of hindgut rotation.


Introduction
Left-right (LR) asymmetry is typically integrated into the basic body plan in bilaterians, in which internal organs are often LR-asymmetric in both morphology and function. The mechanisms of LR-asymmetric development are well studied in vertebrates [1][2][3][4][5]. In mice, for example, motile cilia located in the embryonic ventral node rotate clockwise and induce a leftward flow of extra-embryonic fluid, thereby creating the first break in LR symmetry [6]. This phenomenon, called nodal flow, subsequently induces the left-side-specific expression of genes required for LR-asymmetric organ development, such as Nodal and Lefty [6][7][8]. The mechanisms that break LR symmetry are evolutionarily divergent even among vertebrates; for example, LR-symmetry breaking occurs independently of nodal flow in both reptiles and chickens [9,10]. In invertebrates, chiral cells contribute to LR-asymmetric development (a cell is chiral if its shape cannot be superimposed onto its mirror image) [11][12][13]. In snails and nematodes, the chirality of blastomeres at the initial stage of cleavage determines their subsequent LR-asymmetric arrangement, which consequently directs the LR-asymmetry of the whole body [14,15].

Live Imaging and Laterality Score
The cell membrane of the hindgut epithelium was visualized by UAS-myr::GFP expression driven by byn-Gal4 using the GAL4/UAS system [50]. Drosophila embryos were dechorionated and placed on grape-juice agar plates. Embryos of the appropriate genotypes were selected at early stage 12 under a fluorescence microscope and mounted dorsal-side up on double sticky tape on slide glasses. The embryos were overlaid by oxygen-permeable Halocarbon oil 27 (Sigma-Aldrich, St. Louis, MO, USA) and a coverslip, using other coverslips of the appropriate thickness as spacers (0.17-0.25 mm). Live images of apical cell boundaries in the hindgut epithelium were obtained with an LSM 880 scanning laser confocal microscope before the onset of hindgut rotation. The embryo was then cultured at 25 • C for 3 h, at which point the rotational direction of the hindgut was evaluated, and the embryo was assigned a laterality score of 1 (counterclockwise), 0 (clockwise), or 0.5 (no rotation).

Analysis of Cell Chirality Index
Cell chirality was analyzed as previously described [29]. Briefly, we obtained images of the apical cell boundaries, detected by Myr::GFP signal, in the dorsal part of the embryonic hindgut just before its rotation (at stage 12) using the LSM 880 confocal microscope (Carl Zeiss, Oberkochen, Germany). Based on these images, we determined the angle (θ) between the anterior-posterior axis of the hindgut tube and each cell boundary using ImageJ Fiji v.2.0.0 [51]. To quantify the LR-asymmetric slanting of the apical cell boundaries in the hindgut epithelial cells, we calculated the cell chirality index as (N R − N L )/(N R + N L ), where N R was the number of boundaries with 0 • < θ < 90 • or −180 • < θ < −90 • , and N L was the number of boundaries with −90 • < θ < 0 • or 90 • < θ < 180 • , for each embryo. The chirality index was measured in a double-blind manner, in which the person analyzing the cell boundaries did not know the genotype of the embryo or the prospective rotational direction of the hindgut.

Statistical Analysis
We used logistic models to test the correlation between the mean cell-chirality index and the mean laterality score in fixed embryos or between the live cell-chirality index and the laterality score in each living embryo [52]. As a null hypothesis, we used naïve models [52]. For the fixed embryos, the mean laterality score was treated as a response variable, and the mean fixed cell-chirality index was treated as an explanatory variable. For the live embryos, the laterality score of each individual embryo (0, 0.5, or 1) was treated as a response variable, and the live cell-chirality index of each was treated as an explanatory variable. All statistical analyses were performed using R software v.3.6.3 [53]. Graphs were prepared using Matplotlib v.3.0.3 in Python v.3.6.4 [54,55].

A Logistic Model Significantly Explained the Correlation between the Enantiomorphic States of Chiral Cells and the LR-Directionality of Hindgut Rotation
The Drosophila hindgut is first formed as a bilaterally symmetric invagination in which the anterior part curves ventrally at early stage 12 ( Figure 1A, left panel) [17]. Then, it gradually rotates counterclockwise 90 • as viewed from the posterior ( Figure 1A, middle panels). This rotation causes the hindgut to curve toward the right at the end of stage 13 ( Figure 1A, right-most panel). The hindgut Symmetry 2020, 12, 1991 4 of 12 epithelium has a typical apical-basal polarity, and the inner surface of the hindgut corresponds to the apical surface. Before the rotation of the hindgut, the chirality of the hindgut epithelial cells is detected in the shape of their apical surface, and the frequency of cell boundaries that slant to the left or right relative to the anterior-posterior axis of the hindgut tube deviates according to the genetic conditions [29]. For example, wild-type embryos had more left-than right-slanting cell boundaries ( Figure 1B, left panel). However, there was no LR bias in the angle of cell boundaries when hindgut rotation was complete ( Figure 1B, right panel). We quantitatively analyzed cell chirality using a previously formulated chirality index [29]. The apical cell boundaries were visualized, and two-dimensional coordinates corresponding to the anterior-posterior and left-right axes were placed on a vertex as the origin ( Figure 1C  detected in the shape of their apical surface, and the frequency of cell boundaries that slant to the left or right relative to the anterior-posterior axis of the hindgut tube deviates according to the genetic conditions [29]. For example, wild-type embryos had more left-than right-slanting cell boundaries ( Figure 1B, left panel). However, there was no LR bias in the angle of cell boundaries when hindgut rotation was complete ( Figure 1B, right panel). We quantitatively analyzed cell chirality using a previously formulated chirality index [29]. The apical cell boundaries were visualized, and twodimensional coordinates corresponding to the anterior-posterior and left-right axes were placed on a vertex as the origin ( Figure 1C  The hindgut has a bilaterally symmetric structure in which the anterior part curves ventrally at early stage 12. In the wild-type embryo, the hindgut subsequently rotates counterclockwise, causing the organ to curve to the right. At the end of stage 13, the hindgut has a hook shape pointing toward the right. L, left; R, right. (B) Apical cell boundaries in the wild-type hindgut (orange lines) prior to hindgut rotation tend to slant to the left, which is defined as dextral cell chirality. After hindgut rotation, these cells are no longer chiral, but are instead LRsymmetric (gray lines). (C) Schemas that summarize the procedure used to calculate the cell chirality index. The angle between each boundary and the anterior-posterior (AP) axis of the hindgut was determined. LR represents the left-right axis of the hindgut. Each boundary was classified as righttilted (orange) or left-tilted (turquoise), and the cell chirality index was calculated from the number . The hindgut has a bilaterally symmetric structure in which the anterior part curves ventrally at early stage 12. In the wild-type embryo, the hindgut subsequently rotates counterclockwise, causing the organ to curve to the right. At the end of stage 13, the hindgut has a hook shape pointing toward the right. L, left; R, right. (B) Apical cell boundaries in the wild-type hindgut (orange lines) prior to hindgut rotation tend to slant to the left, which is defined as dextral cell chirality. After hindgut rotation, these cells are no longer chiral, but are instead LR-symmetric (gray lines). (C) Schemas that summarize the procedure used to calculate the cell chirality index. The angle between each boundary and the anterior-posterior (AP) axis of the hindgut was determined. LR represents the left-right axis of the hindgut. Each boundary was classified as right-tilted (orange) or left-tilted (turquoise), and the cell chirality index was calculated from the number of right-tilted (N R ) and left-tilted (N L ) boundaries using the formula shown on the right side of the figure.
Scale bars in A are 25 µm.

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We previously showed that the mean cell-chirality index strongly correlates with the percentage of normal hindgut laterality in embryos with various genotypes [29]. To investigate a causal association between the enantiomorphic states of chiral cells and the LR-direction of hindgut rotation, we here analyzed the mathematical characteristics of the correlation between the mean cell-chirality index and the rotational direction of the hindgut. We assigned each embryo a laterality score based on the rotational direction of the hindgut, as 1 (normal LR asymmetry), 0.5 (non-laterality; i.e., bilateral symmetry), or 0 (inverse LR asymmetry) (Figure 2A). We calculated the mean laterality score for all embryos with the same genotype ( Figure 2B; the number of embryos is shown as N x ). Besides the eight genetic conditions analyzed in the previous study, we examined two additional conditions-double mutant embryos of da 10 and emc AP6 (da 10 ; emc AP6 ) and MyoIC overexpressing embryos (NP2432 > MyoIC)-to study the correlation between the mean cell-chirality index and the mean laterality score ( Figure 2B) [29]. Our previous analysis revealed that a da mutation suppresses LR defects of the hindgut in the emc mutant because its LR defects are induced through da hyperactivation [29]. We also examined embryos overexpressing UAS-MyoIC, which leads to sinistral LR-asymmetric development in the hindgut epithelium ( Figure 2B) [26,40,41]. We previously showed that the mean cell-chirality index strongly correlates with the percentage of normal hindgut laterality in embryos with various genotypes [29]. To investigate a causal association between the enantiomorphic states of chiral cells and the LR-direction of hindgut rotation, we here analyzed the mathematical characteristics of the correlation between the mean cell-chirality index and the rotational direction of the hindgut. We assigned each embryo a laterality score based on the rotational direction of the hindgut, as 1 (normal LR asymmetry), 0.5 (non-laterality; i.e., bilateral symmetry), or 0 (inverse LR asymmetry) (Figure 2A). We calculated the mean laterality score for all embryos with the same genotype ( Figure 2B; the number of embryos is shown as Nx). Besides the eight genetic conditions analyzed in the previous study, we examined two additional conditions-double mutant embryos of da 10 and emc AP6 (da 10 ; emc AP6 ) and MyoIC overexpressing embryos (NP2432 > MyoIC)-to study the correlation between the mean cell-chirality index and the mean laterality score ( Figure 2B) [29]. Our previous analysis revealed that a da mutation suppresses LR defects of the hindgut in the emc mutant because its LR defects are induced through da hyperactivation [29]. We also examined embryos overexpressing UAS-MyoIC, which leads to sinistral LR-asymmetric development in the hindgut epithelium ( Figure 2B) [26,40,41]. The dotted line indicates the logistic model that best fits the data. Some data were adopted from our previous paper [29]. Genotypes are shown in the right panel. Nx and Ny indicate the number of embryos used to analyze the mean cell-chirality index and the mean laterality score, respectively. R 2 , coefficient of determination; p < 0.001, two-tailed t-test.
We fitted the logistic model ( Figure 2B, dotted line) with the cell chirality index as an explanatory variable and the mean laterality score as an objective variable ( Figure 2B). The chirality index significantly explained the mean laterality score [quasibinomial generalized linear model (GLM); two-tailed t-test, p < 0.001] ( Figure 2B; Table A1). hindgut (shown in orange) demonstrating normal LR asymmetry, non-laterality (bilateral symmetry), and inverse LR asymmetry, which were scored as 1, 0.5, and 0, respectively. (B) Graph showing the correlation between the mean cell-chirality index and the mean laterality score; colored circles show mean values, and colored lines show standard error. The dotted line indicates the logistic model that best fits the data. Some data were adopted from our previous paper [29]. Genotypes are shown in the right panel. N x and N y indicate the number of embryos used to analyze the mean cell-chirality index and the mean laterality score, respectively. R 2 , coefficient of determination; p < 0.001, two-tailed t-test.
We fitted the logistic model ( Figure 2B, dotted line) with the cell chirality index as an explanatory variable and the mean laterality score as an objective variable ( Figure 2B). The chirality index significantly explained the mean laterality score [quasibinomial generalized linear model (GLM); two-tailed t-test, p < 0.001] ( Figure 2B; Table A1).

The Cell Chirality Index Predicts the LR-Directions of Future Hindgut Rotation in Live Embryos
Considering that cell chirality appears before hindgut rotation is initiated, the significant correlation found between the mean cell-chirality index and the mean laterality score suggested that an individual embryo's cell chirality index might determine the LR directionality of its hindgut rotation. In this case, the individual's cell chirality index should predict the left or right directionality of the upcoming Symmetry 2020, 12, 1991 6 of 12 hindgut rotation. To test this possibility, we developed a new procedure to ascertain the cell chirality index in the hindgut of live embryos and to determine the subsequent LR directionality of the hindgut rotation. In this system, the apical cell boundaries of the hindgut epithelium were visualized in live embryos at early stage 12 under a confocal laser microscope. The embryos were cultured for another three hours (when hindgut rotation would be complete in wild-type embryos), at which point we examined the direction of hindgut rotation ( Figure 3A, right panel). The live cell-chirality index was calculated for each embryo using the live-imaging data from early stage 12, and the embryo was assigned a laterality score of 1 (normal LR asymmetry), 0.5 (non-laterality), or 0 (inverse LR asymmetry), according to the direction of the subsequent hindgut rotation.

The Cell Chirality Index Predicts the LR-Directions of Future Hindgut Rotation in Live Embryos
Considering that cell chirality appears before hindgut rotation is initiated, the significant correlation found between the mean cell-chirality index and the mean laterality score suggested that an individual embryo's cell chirality index might determine the LR directionality of its hindgut rotation. In this case, the individual's cell chirality index should predict the left or right directionality of the upcoming hindgut rotation. To test this possibility, we developed a new procedure to ascertain the cell chirality index in the hindgut of live embryos and to determine the subsequent LR directionality of the hindgut rotation. In this system, the apical cell boundaries of the hindgut epithelium were visualized in live embryos at early stage 12 under a confocal laser microscope. The embryos were cultured for another three hours (when hindgut rotation would be complete in wildtype embryos), at which point we examined the direction of hindgut rotation ( Figure 3A, right panel). The live cell-chirality index was calculated for each embryo using the live-imaging data from early stage 12, and the embryo was assigned a laterality score of 1 (normal LR asymmetry), 0.5 (nonlaterality), or 0 (inverse LR asymmetry), according to the direction of the subsequent hindgut rotation.  To investigate whether the live cell-chirality index correlates with the rotational direction of the hindgut, we used emc AP6 homozygotes, which have an LR-randomization phenotype. Of the ten different mutants examined in this study, the emc AP6 mutant was unique in having a mean cell-chirality index of nearly zero with deviations in both the plus and minus values ( Figure 2B). In addition, the hindgut in these embryos can develop with normal or inverse LR asymmetry or with a non-lateral phenotype [29]. Thus, we speculated that cell chirality varies stochastically between individual embryos, and that each embryo's predominant cell chirality might induce the hindgut to rotate in the corresponding direction. Based on this assumption, we evaluated the consistency of cell chirality indexes obtained from individual fixed and live emc AP6 homozygous embryos, and compared the mean cell-chirality index for live wild-type and emc AP6 homozygous embryos. There was no significant difference in the mean live cell-chirality indexes for wild-type (−0.12 ± 0.04) and emc AP6 homozygous embryos (−0.02 ± 0.03; two-tailed t-test, p = 0.069217), and the values were similar to those reported previously for fixed embryos (wild-type −0.11 ± 0.03; emc AP6 homozygote 0.01 ± 0.02) [29]. We also found that the live cell-chirality index varied widely for individual emc AP6 homozygotes, with both plus and minus values, unlike that of wild-type embryos ( Figure 3B).
Given that the values of the cell-chirality indexes agreed well between live and fixed embryos, we next analyzed statistical correlations between the live cell-chirality index and the laterality score for each emc AP6 -mutant embryo. We fitted the logistic model (solid line, Figure 3B) with the live chirality index as an explanatory variable and the laterality score of each embryo as an objective variable and found that live cell chirality, which was determined prior to the onset of hindgut rotation, significantly explained the LR-directionality of rotation [quasibinomial GLM, two-tailed t-test, p < 0.01] ( Figure 3C; Table A2). Importantly, the logistic model obtained for fixed embryos (Figures 2B and 3C, dotted line) with the genetic conditions described in Figure 2 significantly fitted the data obtained from each living emc AP6 -mutant embryo [quasibinomial GLM, likelihood ratio test, χ 2 1 = 4.327, p < 0.05], and the model explained 72.5% of the total variation in the hindgut rotational direction in live emc AP6 -mutant embryos (Table A3). These results suggested that the cell chirality index correlates with the rotational direction of the hindgut, regardless of whether enantiomorphic states of chiral cells are determined by genetics or stochastic fluctuations. Based only on the statistical correlation, we could not conclude whether cell chirality was the cause or effect; however, given the clear chronological sequence of the formation of cell chirality and the initiation of hindgut rotation, we concluded that the enantiomorphic states of chiral cells direct the LR-asymmetry of hindgut rotation.

Discussion
Previous studies suggest that the enantiomorphic state of chiral cells in the Drosophila hindgut epithelium determines the direction of hindgut rotation, with an average dextral or sinistral cell chirality leading to a counterclockwise or clockwise rotation, respectively [25,27,29]. This postulation was first supported by the observation that the mean state of cell chirality correlates to the LR-direction of hindgut rotation in various mutants [25,27,29]. For example, in MyoID mutants, which develop sinistral cell chirality, the hindgut rotates clockwise, whereas wild-type embryos show dextral cell chirality and a counterclockwise rotation [27]. In Drosophila E-cadherin or emc mutants, which have no cell chirality on average, the LR-direction of hindgut rotation is randomized or the hindgut remains LR-symmetric [27,29]. Additional support for this postulation comes from computer vertex-model simulations in which the initial enantiomorphic state of chiral cells introduced into the model defines the LR-direction of the model gut-tube rotation and successively drives tube rotation in the direction determined at the outset [27]. Although studies have consistently reported an apparent concordance between the state of cell chirality and the LR-directionality of hindgut rotation, supported by predictions from computer simulations [25,27], a cause-and-effect relationship has not previously been verified.
To address this issue, in this article we mathematically evaluated this hypothetical causal relationship by analyzing the correlation between the enantiomorphic states of chiral cells and the LR-direction of hindgut rotation. We examined fixed embryos to determine the mean cell-chirality index and laterality Symmetry 2020, 12, 1991 8 of 12 score for each of ten different genetic conditions, and analyzed the correlation between the cell-chirality index and laterality score. In our logistic model, the mean cell-chirality index, representing each genotype as an explanatory variable, significantly fitted with the mean laterality score ( Figure 2B). Therefore, the mechanisms by which cell chirality defines the LR-directionality of hindgut rotation may be similar, regardless of the genetic background. This result also demonstrates that the LR-directionality of hindgut rotation is statistically explained by just the enantiomorphic state of chiral cells as averaged for embryos of the same genotype.
In correlation analysis of fixed embryos, the mean cell-chirality index of emc AP6 -mutant embryos was 0.01 ± 0.02; however, all three hindgut-rotation phenotypes-clockwise, counterclockwise, and bilaterally symmetric-were evident among the embryos ( Figure 2B) [29]. Thus, one could argue that cell chirality might not be essential for directing hindgut rotation. Our analyses here addressed this question. In this study, we developed a method to determine the live cell-chirality index and the direction of the hindgut rotation in each living embryo. We found that the live cell-chirality indexes representing individual emc AP6 mutant embryos varied widely, being distributed from plus to minus values, although the mean value of these embryos' live cell-chirality index was nearly zero ( Figure 3B). Therefore, this mutant background was particularly useful for analyzing the correlation between the states of cell chirality and the rotational direction of the hindgut in each live embryo. Our logistic model formulated from the data of the live emc AP6 mutant embryos showed a significant correlation between the live cell-chirality index and the laterality score of individual embryos ( Figure 3C). Therefore, in each of these embryos, the live cell-chirality index significantly explained the rotational direction of the hindgut. Based on these results, we ascertained that the cell chirality is not only sufficient, but also required for the hindgut rotation, because our model predicts that living embryos with a zero cell-chirality index tend to have a bilaterally symmetric hindgut.
Importantly, the logistic model obtained from fixed embryos with various genetic conditions significantly fitted the data obtained from each living emc AP6 -mutant embryo [quasibinomial GLM, likelihood ratio test, χ 2 1 = 4.327, p < 0.05], and 72.5% of the total variation in the rotational direction of the emc AP6 -mutant hindgut could be explained by the model ( Figure 3C; Table A3), while 27.5% of that was explained by residuals. Given the wide range of live cell-chirality indexes in individual embryos from the same emc AP6 -mutant background, cell chirality may be formed stochastically in each individual under this condition. Nevertheless, the logistic model formulated from the data from fixed embryos of various genotypes significantly explains the data that presumably reflect stochastic events in each emc AP6 individual. Therefore, the underlying mechanisms by which cell chirality drives the LR-directional hindgut rotation are common between genetically or stochastically formed cell chirality.
In this study, we mathematically confirmed the causal relationship between cell chirality and the direction of hindgut rotation. Our logistic model also implies that cell chirality is sufficient and necessary for the hindgut rotation. Considering the time course of the events, in which cell chirality is formed before the initiation of the hindgut rotation in vivo, our results presented here demonstrate that cell chirality is the primary cause of the hindgut rotation. Since cell chirality is involved in the LR-asymmetric development of various organs in Drosophila, such a cause-and-effect relationship can also be applied to explain their morphogenesis. Furthermore, our idea could extend to LR-asymmetric development involving chiral cells in other species. Funding: This study was supported by Japan Society for the Promotion of Science KAKENHI Grants (#16J01027 to T.I., #18K06255 to M.I., and #15H05856 and #15H05863 to K.M.) Stock Center (Kyoto Institute of Technology) for fly stocks, and the Developmental Studies Hybridoma Bank (University of Iowa) for antibodies.

Conflicts of Interest:
The authors declare no conflict of interest.  Table A3. Logistic regression analyses between the laterality score and live cell-chirality index in emc AP6 mutants.

R 2
Best fit model 1 −