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

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fly Lines

^{AP}

^{6}, an amorphic allele (Bloomington #36544) [43]; da

^{10}, an amorphic allele (Bloomington #5531) [44]; and MyoID

^{K}

^{2}, an amorphic allele [45]. The following UAS lines were used: UAS-emc::GFP [46]; UAS-da (Bloomington #51669) [47]; UAS-MyoIC [17]; UAS-MyoID::mRFP [28]; and UAS-myr::GFP [48]. The following Gal4-driver lines were used: NP2432 (Kyoto DGRC #104201) [49] to analyze the fixed cell-chirality index, and byn-Gal4 [17] to analyze the live cell-chirality index. Mutations on the second and third chromosomes were balanced with CyO, P{en1}wg

^{en}

^{11}and with TM3, P{GAL4-twi.G}2.3, P{UAS-2xEGFP}AH2.3, Sb

^{1}Ser

^{1}, respectively. All genetic crosses were carried out at 25 °C on a standard Drosophila culture medium.

#### 2.2. Live Imaging and Laterality Score

#### 2.3. Analysis of Cell Chirality Index

_{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.

#### 2.4. Statistical Analysis

## 3. Results

#### 3.1. A Logistic Model Significantly Explained the Correlation between the Enantiomorphic States of Chiral Cells and the LR-Directionality of Hindgut Rotation

_{R}) and N-Left (N

_{L}), respectively (Figure 1C, right panel). The mean cell-chirality index was calculated from the values obtained for all embryos of the same genotype.

_{x}). Besides the eight genetic conditions analyzed in the previous study, we examined two additional conditions—double mutant embryos of da

^{10}and emc

^{AP}

^{6}(da

^{10}; emc

^{AP}

^{6}) 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].

#### 3.2. The Cell Chirality Index Predicts the LR-Directions of Future Hindgut Rotation in Live Embryos

^{AP}

^{6}homozygotes, which have an LR-randomization phenotype. Of the ten different mutants examined in this study, the emc

^{AP}

^{6}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

^{AP}

^{6}homozygous embryos, and compared the mean cell-chirality index for live wild-type and emc

^{AP}

^{6}homozygous embryos. There was no significant difference in the mean live cell-chirality indexes for wild-type (−0.12 ± 0.04) and emc

^{AP}

^{6}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

^{AP}

^{6}homozygote 0.01 ± 0.02) [29]. We also found that the live cell-chirality index varied widely for individual emc

^{AP}

^{6}homozygotes, with both plus and minus values, unlike that of wild-type embryos (Figure 3B).

^{AP}

^{6}-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 (Figure 2B and Figure 3C, dotted line) with the genetic conditions described in Figure 2 significantly fitted the data obtained from each living emc

^{AP}

^{6}-mutant embryo [quasibinomial GLM, likelihood ratio test, ${\chi}_{1}^{2}=4.327$, p < 0.05], and the model explained 72.5% of the total variation in the hindgut rotational direction in live emc

^{AP}

^{6}-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.

## 4. Discussion

^{AP}

^{6}-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

^{AP}

^{6}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

^{AP}

^{6}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.

^{AP}

^{6}-mutant embryo [quasibinomial GLM, likelihood ratio test, ${\chi}_{1}^{2}=4.327$, p < 0.05], and 72.5% of the total variation in the rotational direction of the emc

^{AP}

^{6}-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

^{AP}

^{6}-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

^{AP}

^{6}individual. Therefore, the underlying mechanisms by which cell chirality drives the LR-directional hindgut rotation are common between genetically or stochastically formed cell chirality.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Factors affecting variations in the laterality score of the embryonic hindgut in various Drosophila genotypes.

${\mathit{t}}_{8}-\mathbf{Value}$ | p-Value | |
---|---|---|

Intercept | −4.042 | 0.003723 |

Chirality Index | −5.992 | 0.000326 |

**Table A2.**Factors affecting variations in the rotational direction of the hindgut in emc

^{AP}

^{6}mutants.

${\mathit{t}}_{13}-\mathbf{Value}$ | p-Value | |
---|---|---|

Intercept | −1.149 | 0.27109 |

Live Chirality Index | −3.256 | 0.00625 |

**Table A3.**Logistic regression analyses between the laterality score and live cell-chirality index in emc

^{AP}

^{6}mutants.

Model | ${\mathit{R}}^{2}$ | |
---|---|---|

Best fit model | $1-\frac{1}{1+{e}^{-4.531\times \left(x-0.00697\right)}}$ | 0.8607872 |

Model fitted for Figure 2 | $1-\frac{1}{1+{e}^{-0.410\times \left(x-3.42\right)}}$ | 0.7246853 |

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**Figure 1.**The wild-type Drosophila embryonic hindgut rotates 90° counterclockwise. (

**A**) The Drosophila embryonic hindgut (orange), visualized by the expression of UAS-myr-GFP (which encodes a cell-membrane marker) driven by byn-Gal4. 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.

**Figure 2.**Cell chirality significantly explains the hindgut LR-asymmetry of fixed embryos with various genotypes. (

**A**) Typical examples of the 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.

**Figure 3.**The live cell-chirality index predicts the rotational direction of the hindgut. (

**A**) Typical images of the hindgut in live embryos, showing cell boundaries visualized by UAS-myr::GFP driven by byn-Gal4 in the hindgut epithelium. At early stage 12, the cell-chirality index of the living hindgut epithelial cells was calculated based on a high-magnification image of the region outlined by the orange square (left panel). After imaging, the embryos were incubated for 3 h, at which point each embryo was examined and assigned a laterality score of 1 (normal LR-asymmetry of the hindgut), 0.5 (bilateral symmetry), or 0 (inverse LR-asymmetry). (

**B**) Box plot of the live-cell chirality index of the hindgut in the wild-type and emc

^{AP}

^{6}mutant embryos, showing the number of embryos analyzed (N) and the p-value (two-tailed t-test). (

**C**) Graph showing the correlation between the live cell-chirality index and the laterality score of the hindgut in the emc mutant. The solid line indicates the best-fitted logistic model (Table A2). The dotted line indicates the logistic model obtained from fixed embryos in Figure 2. R

^{2}, coefficient of determination; N, the number of embryos analyzed.

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Ishibashi, T.; Inaki, M.; Matsuno, K. Statistical Validation Verifies That Enantiomorphic States of Chiral Cells Are Determinant Dictating the Left- or Right-Handed Direction of the Hindgut Rotation in *Drosophila*. *Symmetry* **2020**, *12*, 1991.
https://doi.org/10.3390/sym12121991

**AMA Style**

Ishibashi T, Inaki M, Matsuno K. Statistical Validation Verifies That Enantiomorphic States of Chiral Cells Are Determinant Dictating the Left- or Right-Handed Direction of the Hindgut Rotation in *Drosophila*. *Symmetry*. 2020; 12(12):1991.
https://doi.org/10.3390/sym12121991

**Chicago/Turabian Style**

Ishibashi, Tomoki, Mikiko Inaki, and Kenji Matsuno. 2020. "Statistical Validation Verifies That Enantiomorphic States of Chiral Cells Are Determinant Dictating the Left- or Right-Handed Direction of the Hindgut Rotation in *Drosophila*" *Symmetry* 12, no. 12: 1991.
https://doi.org/10.3390/sym12121991