Revealing chiral cell motility by 3D Riesz transform-differential interference contrast microscopy and computational kinematic analysis

Left–right asymmetry is a fundamental feature of body plans, but its formation mechanisms and roles in functional lateralization remain unclear. Accumulating evidence suggests that left–right asymmetry originates in the cellular chirality. However, cell chirality has not yet been quantitatively investigated, mainly due to the absence of appropriate methods. Here we combine 3D Riesz transform-differential interference contrast (RT-DIC) microscopy and computational kinematic analysis to characterize chiral cellular morphology and motility. We reveal that filopodia of neuronal growth cones exhibit 3D left-helical motion with retraction and right-screw rotation. We next apply the methods to amoeba Dictyostelium discoideum and discover right-handed clockwise cell migration on a 2D substrate and right-screw rotation of subcellular protrusions along the radial axis in a 3D substrate. Thus, RT-DIC microscopy and the computational kinematic analysis are useful and versatile tools to reveal the mechanisms of left–right asymmetry formation and the emergence of lateralized functions.

Some specific comments: Page 8: "By visual observation, individual filopodia not only twirled in the direction of a right-handed screw as previously reported but also appeared to exhibit axial spinning. They seemed to show retrograde motion toward the growth cone body, consistent with the retrograde actin flow." I simply don't see this from the figure or the movies. Fig. 4d is supposed to show us that right-screw rotation is dominant over left-screw. I don't quite see that; there are too many colors in the figure. Also, the quantification of this is in Fig 4g. Presumably, the values next to the distribution represent the average and SD. The average is slightly positive which, I guess, means right-screw dominance. This is not explained. Furthermore, the average is very close to zero, can we really draw any conclusions from this? In other words, do we know that this distribution is skewed in a statistically significant way? Why are the numbers of Fig. 4e and table 4i different? Do they represent different velocity magnitudes? Fig. 5: the velocity distribution is more skewed than the one in Fig. 4 but, again, how do we know that this skewness is statistically significant? Fig. 6: Please show a quantitative analysis of the cell trajectories, including the biased clockwise motion. Also, how do cell-cell collision affect this bias? Furthermore, how is the non-zero rotational motion along an axis perpendicular to the surface going to result curved trajectories? A more mechanistic insight will be helpful. Fig. 7: This seems to show that a Dictyostelium cell has many tips. Normally, in 2D motion, it is believed that these cells have only 1-3 pseudopods. See, for example, Bosgraaf and van Haastert, Plos One, 2009. Please comment. Also, how is a tip defined and how is the radial axis defined? I also have a conceptual difficulty with this figure. It seems to show a right-screw rotation around the axis of motility. Fig. 6 seems to show a right-screw rotation perpendicular to the axis of motility. How are these two related? Ref. 45 is not relevant to the clockwise or anti-clockwise motion of Dictyostelium aggregates. A better one is Rappel et al, Phys. Rev. Lett. 1999.

Reviewer #2 (Remarks to the Author):
My review will concentrate on the microscopy aspects of the manuscript. This manuscript proposes a composite Riesz transform (RT) operator to visualise and analyse single-shot DIC images. DIC microscopy produces images which are a non-linear mixture of the object amplitude and phase gradient. For transparent specimens with varying refractive index, the phase gradient enables imaging of changes in optical path length, but the resulting images have a shadow cast appearance which complicates the application of visualisation and analysis methods that are often designed for brightness images rather than gradient images.
The composite RT operator proposed in this manuscript is used to convert the shadow cast appearance to a more conventional brightness signal, which can then be thresholded for 3D volume visualisation and analysed using computer vision algorithms. The computer vision analysis has been used to produce comprehensive statistics of the left-right asymmetry of motion and growth in multiple samples of multiple organisms.
The combination and adaptation of methods from multiple disciplines is impressive and well described, and offers an insight into the origins and mechanisms of left-right asymmetry. A key advance in this manuscript is the introduction of a composite RT which enables the use of singleshot DIC capture to collect and subsequently analyse structural information. Single-shot methods are highly valuable for rapid capture of living 3D cells. I think the paper has the potential to be highly influential in demonstrating the application of advanced microscopy and image processing methods to a compelling biomedical problem.
The authors are careful to introduce the topics of image processing of DIC images and, separately, the Riesz transform. However, there is a significant history of application of the Riesz transform specifically to DIC images, which is currently not referenced at all: • Applying the inverse Riesz transform to images captured using an optical variant of DIC was first proposed in (Arnison, 2004) where it was used to integrate the phase gradient to estimate the linear phase. • A recent paper by (Shribak, 2017) proposes using the inverse Riesz transform for visualisation of images captured using another optical variant of DIC. This paper also serves as a brief review of the last 13 years of literature on Riesz transforms and DIC. Although I have listed papers which use the inverse RT, the forward and inverse RT operations are closely related.
These papers all rely on multi-shot variants of DIC, so the use of the RT with single-shot DIC in the manuscript remains novel. The claims on page 14 that the proposed method can be used with standard a DIC microscope are justified.
An additional issue is that while the manuscript correctly cites (Felsberg, 2001), the Riesz transform as a 2D extension of the 1D Hilbert transform was independently and simultaneously proposed by (Larkin, 2001). The manuscript specifically relies on a directional RT, which was introduced by .
Given the importance of the RT to the methods of the paper, and the weight being placed on the novelty of the RT being used in this context, I would recommend revisions be made to clarify the relationship between the composite RT method proposed in the manuscript, and the literature on RT and DIC.
I also have some minor comments and suggestions: 1. Page 19, Line 402: "the intensity was expanded to a full 12-bit range." What does expanded mean? The camera captured data at 12-bit, so working in 12-bits during processing is merely maintaining, not expanding, the range. In addition, I would expect that the Fourier processing described would likely be performed in MATLAB in single precision float (32-bit). 2. Page 20, lines 413-414. The images were "often" deconvolved. Please clarify "often", as this is overly vague. Deconvolution requires a calibrated or estimated PSF. How was the PSF determined?

Reviewer #3 (Remarks to the Author):
Review: From the point of view of DIC image handling for visualization and conversion of DIC -imaged structures into "bright objects" the proposed scheme is understandable. However, it seems partly empirically designed as a deeper foundation of the presented approach in signal/image processing is missing. There should theoretical foundations and connections, as well as discussion of local orientation estimation be included like given in for example in: The theoretical background and novelty to existing reconstruction approaches based on Riesz Transform and/or Hilbert transform is not completely reviewed. This part should particularly be improved and extended. Discuss novelty, similarities, and differences of presented approach to publications like: In this paper, the authors present new applications of existing image analysis and signal processing techniques. In particular, they apply these techniques to determine whether cells display chiral biases. I appreciate the topic and the goal of the paper.
However, the article is difficult to follow and the figure are not so convincing.
Furthermore, the number of movies is overwhelming and they are not helpful. I would urge the authors to make their study more readable and to display the results in a clearer and more intuitive fashion.

[Answer to General Comment #1]
We are thankful to the reviewer for constructive comments on the manuscript. As depicted by the reviewer, our original manuscript was somewhat weak in clear description and data presentation. Following the suggestions by the reviewer, we have made the manuscript clearer and more readable in this revision. The major improved points are as follows: 1. Statistical data presentation might be confusing as pointed out by the reviewer. We used two levels of data; "individual" data and "summary" data. Individual data were collected from large samples (mostly from a large number of pixels or voxels) that were obtained in individual experimental trials (cells or cultures). Because these data do not follow a normal distribution, their bias from zero values was statistically tested by the non-parametric Wilcoxon signed-rank test. Summary data were composed of the mean values of the individual data. Their sample number is equal to the number of experimental trials. Because the summary data follow a normal distribution as predicted by "The Central Limit Theorem", their bias from zero was tested by the parametric one-sample t-test. To avoid a confusion and misunderstanding of readers, we have clearly stated the explanation of the two categories and the ways of statistical testing in the revised manuscript. In addition, we have presented the summary data only in the bar graphs of the main figures. All of the individual data were moved to Supplementary Information (data statistics to Supplementary Table 2 2. We have reduced the number of movies from 20 to 12, as suggested by the reviewer.
Movies that are not essential were removed. Movies representing different views of the same samples were presented side-by-side in single movies to facilitate the understanding of the readers.
3. We have reduced the number of colors from the pictures. We used a combination of red/blue/gray instead of red/blue/green ( Fig. 4 and 7). We have also reduced unnecessary colors from the drawings as many as possible.
4. As depicted by the reviewer, it seems difficult for readers to conceptually understand the relationship between the chiral phenomena described in separate sections of the original manuscript. In the revised manuscript, we have added a new figure (Fig. 8) that explains a schematic model on the relationship between a series of chiral behaviors with description of previously-known, newly-found and presumptive mechanistic insights. This figure will facilitate the understanding of the readers.

[Answer to Specific Comment #1-1]
As mentioned by the reviewer, it might be difficult for the readers to visually percept 3D motion from these movies. Thus, we have performed particle tracking analysis by [Answer to Specific Comment #1-2] As mentioned in Answer to General Comment #1, we removed green color from the pictures by replacing it with gray color. We also added a picture showing RT-DIC intensity alone with gray color in Fig. 4a, and a picture showing velocity magnitude in

[Specific Comment #1-3]
Also, the quantification of this is in Fig 4g. Presumably, the values next to the distribution represent the average and SD. The average is slightly positive which, I guess, means right-screw dominance. This is not explained. Furthermore, the average is very close to zero, can we really draw any conclusions from this? In other words, do we know that this distribution is skewed in a statistically significant way?

[Answer to Specific Comment #1-3]
We thank the reviewer for pointing out our failure. We forgot to explain the meaning of the values (mean ± s.d) in Fig. 4e-g of the original manuscript. In the revised manuscript, these histograms were moved to Supplementary Fig. 5a- Statistics of all "individual" data including those of the example (cell #2) shown in the histograms were listed in Supplementary Table 2. All axial data were statistically tested for the null hypothesis that the median value is equal to zero by the non-parametric Wilcoxon signed-rank test (Supplementary Table 2). The results indicate that almost all of the individual axial data (both axial velocity and axial angular velocity data) are significantly biased from zero with low P-values (P<0.0001).

[Specific Comment #1-4]
Why are the numbers of Fig. 4e and  among all voxels in all frames (n=2.17 × 10 7 voxels) of cell #2, which is shown in the pictures of Fig. 4b,d. This is an example of "individual" data. On the other hand, the numbers in Fig. 4i show the "summary" data that represent the mean ± s.e.m. of the mean of the individual cell data (n=8 cells). In the revised manuscript, the numbers at the bottom of the picture Fig. 4b,d,e represent the individual data of cell #2 (same as the numbers in the old Fig. 4e-g), while the graphs in the new Fig. 4f represent the summary data from 8 cells. We have rewritten the legends of Fig. 4 so that these differences are clearly understood.
[Specific Comment #1-5] Fig. 5: the velocity distribution is more skewed than the one in Fig. 4 but, again, how do we know that this skewness is statistically significant?

[Answer to Specific Comment #1-5]
We thank the reviewer for pointing out the lack of data on the statistical test. We added the result of the statistical test in Fig. 5f and the legends of the revised manuscript. We found a significant bias from zero values in the signed curvature of this sample (Fig.   5f). Fig. 5 shows a neurite growth pattern in still images taken from an aldehyde-fixed culture sample. We only analyzed the curvature, but not the velocity or angular velocity.
Thus, we do not think that the direct comparison of the skewness among different physical quantities have meanings.
Reading the original manuscript again, we noticed that there was a logical gap between the explanation of 3D helical motion of growth cones in Fig. 4 and that of 2D clockwise neurite growth in Fig. 5, which could give misleading interpretations to the readers on the relationship between these phenomena. Thus, we rewrote the sentences at the top of the section of 2D neurite growth as follows: Page 11, Line 240: "Quantification of chiral pattern in clockwise neurite growth RT-DIC microscopy and the associated methods can be used to automatically analyze chiral patterns in various scales, dimensions and cell types. In the scale larger than the growth cone, the neurons extend neurites clockwise on 2D culture substrates 5, 6 ( Fig.   5a). This 2D clockwise neurite growth is driven by the 3D right-screw rotation of the growth cone filopodia 6 , which is newly found to be accompanied by the 3D helical motion as described in the previous section." We further presented a schematic model in Fig.8 of the revised manuscript. This scheme will help the readers to conceptually understand the hierarchical relationship of chiral behaviors in the neurons.

[Answer to Specific Comment #1-6]
We thank the reviewer for the constructive suggestion that enhances the value of our work. In response to the reviewer's request, we have performed new experiment on the cell tracking analysis. The results are shown as new data and new movies ( Fig. 6d-g,   Supplementary Fig. 6d-f, Supplementary Table 4 and Supplementary Movie 9,10).
We have succeeded in tracking of individual cells moving in 10 mm 2 areas for 9 hours.
Visual inspection of the movies, the cumulative angular displacements (Fig. 6f) and the statistics of the physical quantities (Fig. 6g) clearly and significantly show the clockwise bias. The newly-measured cell-wise quantities are comparable to the previously-measured pixel-wise values.

[Answer to Specific Comment #1-7]
To answer this question, we separately calculated the physical quantities in the presence or absence of cell-cell contacts that were judged from the distance of the cell centroids (Supplementary Table 2 for individual data and Fig. 6g for summary data). We found that the mean values did not differ between the two states, but there was an increase in the variance of the quantities in the contact state. Accordingly, the curvature in the contact state did not show significant bias from zero. These data indicate that the clockwise bias is an intrinsic cell property and that this bias is perturbed by cell-cell contacts. Observation of the movies also revealed that rotational motion of the cells was independent of each other, suggesting that the bias is a cell-autonomous property.

[Specific Comment #1-8]
Furthermore, how is the non-zero rotational motion along an axis perpendicular to the surface going to result curved trajectories? A more mechanistic insight will be helpful.

[Answer to Specific Comment #1-8]
We thank the reviewer for raising the intriguing question. Rotational motion does not always generate a curved trajectory. If the rotation is composed of pure spin around the center of the cell without revolution, the cell center would move straight but each pixel would show cycloid-like complex motion. On the other hand, if the rotation is composed of pure revolution without spin, all pixels including the cell center would form circular trajectories. It is difficult to discriminate between the spin and the revolution from pixel-wise data alone without their integration into cell-wise data. Thus, as suggested by the reviewer, cell-wise tracking data would become of particular importance for detection of the circular trajectories. The cell-wise data obtained in additional experiments (Fig. 6g) actually showed the presence of circular trajectories and a clockwise bias with comparable amount of quantities as similar as the pixel-wise data (Fig. 6c). These results support the presence of some mechanistic factors for generation of the revolution, but not those for the spin. Further mechanistic insights with relation to 3D rotational motion are discussed below in Answer #1-11 and Fig. 8

[Answer to Specific Comment #1-9]
In the analysis of the growth cones, we focused on the filopodia, but not on the lamellipodia. Analogically, in the analysis of Dictyostelium cells, we did not focused on the pseudopods but rather on the finer filopodial processes. Because the protrusions drawn in Fig. 7d of the original manuscript were ambiguous in shape, we replaced them with finer structures that look like filopodia. The diameter of interest can be controlled by the setting of the outer scale of the structure tensor. In the data shown in Fig. 7, we set the scale to the size comparable to the diameter of the filopodia. In preliminary experiments, we also analyzed the motility of the larger scale tip structure that may correspond to pseudopodia, but we could not detect a biased motility in such larger structures. In the revised manuscript, we added the following description with citation of Bosgraaf and Haastert (2009): Page 13, Line 305: "In this study, we focused on fine protrusions including filopodia, but not on pseudopodia 42 , by setting the outer scale of the tensor, which is the diameter of interest, to about 0.6 μm."

[Specific Comment #1-10]
Also, how is a tip defined and how is the radial axis defined?
[Answer to Specific Comment #1-10] As mentioned above, we calculated the structure tensor focused on the structures with specific size (of diameter) at every voxel of 3D images. See Supplementary Note 2 for detailed protocols. Then we calculate the tip certainty Ct for every voxel from the anti-parallel relationship between the eigenvector e3 and polarity vector ep (the equation was described in the new scheme of Fig. 7b). Tip structures were extracted as the voxels with the certainty larger than the fixed threshold.
For the radial axis, we first calculated the intensity-weighted centroid that represents the center of the cell. The radial axis at the point of interest can be uniquely defined as the direction of the line connecting from the centroid to the point of interest (Fig. 7b).

[Specific Comment #1-11]
I also have a conceptual difficulty with this figure. It seems to show a right-screw rotation around the axis of motility. Fig. 6 seems to show a right-screw rotation perpendicular to the axis of motility. How are these two related?

[Answer to Specific Comment #1-11]
We thank the reviewer for depicting an important point. As the reviewer mentioned, the 90 degree conversion of the axis of rotation should be achieved. In the new figure (Fig.   8), we explain a schematic model explaining the conversion from the molecular chirality through 3D helical filopodial motility to 2D clockwise cell motility. See details in Fig. 8 and the legends. Currently, we do not know the detailed molecular mechanisms of the conversion in Dictyostelium cells, but they can be predicted by the analogy with the findings in the neuronal growth cones. The explanation is as follows.
In 2D environments, the filopodia attached to the substrate would not show rotational motion due to physical restriction, but those once detached from the substrate would freely rotate in the right-screw direction within the half hemisphere and attach to the substrate again on the right side. Such motion would generate a rightward bias in the location of the attached filopodia. This asymmetry would cause rightward traction of the cell body, generating clockwise cell migration.

[Specific Comment #1-12]
Ref. 45 is not relevant to the clockwise or anti-clockwise motion of Dictyostelium aggregates. A better one is Rappel et al, Phys. Rev. Lett. 1999.

[Answer to Specific Comment #1-12]
We thank the reviewer for the comment. The reference was replaced with the suggested one in the revised manuscript.

Reviewer 2 [General Comment #2]
The combination and adaptation of methods from multiple disciplines is impressive and well described, and offers an insight into the origins and mechanisms of left-right asymmetry. A key advance in this manuscript is the introduction of a composite RT which enables the use of single-shot DIC capture to collect and subsequently analyse structural information. Single-shot methods are highly valuable for rapid capture of living 3D cells. I think the paper has the potential to be highly influential in demonstrating the application of advanced microscopy and image processing methods to a compelling biomedical problem.

[Answer to General Comment #2]
We are thankful to the reviewer for positive comments that correctly evaluate our work.
We also thank for constructive comments that improve the value of the manuscript. As depicted by the reviewer, one of the most significant points of the paper lies in the development of a single-shot method with the composite RT for rapid DIC imaging. This method will complement the more precise multi-shot methods. In this revision, we have described the historical backgrounds of DIC imaging and Riesz transform and have emphasized the similarity and the novelty of our new methods with relation to the other methods, with citing the literature raised by the reviewer.

[Specific Comment #2-1]
The authors are careful to introduce the topics of image processing of DIC images and, separately, the Riesz transform. However, there is a significant history of application of the Riesz transform specifically to DIC images, which is currently not referenced at all: • Applying the inverse Riesz transform to images captured using an optical variant of DIC was first proposed in (Arnison, 2004) where it was used to integrate the phase gradient to estimate the linear phase.
• A recent paper by (Shribak, 2017)  "To overcome this problem, many methods have been developed to date (Shribak, Larkin et al. 2017). One of the most efficient and convenient methods adopts acquisition of multiple phase gradient images with orthogonal shears and their integration by Riesz transform (RT) (Arnison, Larkin et al. 2004, Larkin and Fletcher 2014, Shribak, Larkin et al. 2017. RT(Felsberg and Sommer 2001), which was independently and simultaneously proposed as the spiral phase transform , is a multidimensional extension of the 1D Hilbert transform (HT), and has recently been used in many fields of image processing and analysis , Unser and Van De Ville 2009, Bernstein, Bouchot et al. 2013, Püspöki, Storath et al. 2016.
These restoration methods with multiple DIC images precisely restore original images, but they require special equipment and multi-shot image acquisition that is disadvantageous for fast 3D live imaging. A method for single-shot DIC imaging with HT was also developed (Arnison, Cogswell et al. 2000), but it cannot detect objects along the shear direction. Here, we developed a simple but efficient method for single-shot DIC images with a composite Fourier filtering based on the directional RT ). This composite RT, utilizing both phase gradient and absorption information of DIC images, converts a shadow-cast DIC image into a self-luminous intensity image. This improved DIC microscopy with the composite RT, called RT-DIC microscopy, was applied to 3D time-lapse imaging of photosensitive structures."

[Specific Comment #2-2]
These papers all rely on multi-shot variants of DIC, so the use of the RT with single-shot DIC in the manuscript remains novel. The claims on page 14 that the proposed method can be used with standard a DIC microscope are justified.

[Answer to Specific Comment #2-2]
We thank the reviewer for positive comments pointing the novelty of our work. In the revised manuscript, we emphasized this point by adding the following sentences.
Page 15, Line 334: Although RT-DIC microscopy with single-shot imaging is not suitable for complete restoration of shear-independent rotation-invariant images like the techniques with multi-shot imaging (Arnison, Larkin et al. 2004, Larkin and Fletcher 2014, Shribak, Larkin et al. 2017, it is highly advantageous for rapid capture of 3D live images. In addition, RT-DIC microscopy uses a standard conventional DIC microscope and does not require any additional special equipment.

[Specific Comment #2-3]
An additional issue is that while the manuscript correctly cites (Felsberg, 2001), the Riesz transform as a 2D extension of the 1D Hilbert transform was independently and simultaneously proposed by (Larkin, 2001). The manuscript specifically relies on a directional RT, which was introduced by .

[Answer to Specific Comment #2-3]
We correctly cited the papers (Larkin, 2001; in the revised manuscript.
The modified description in Introduction was previously mentioned in Answer #2-1.

[Specific Comment #2-4]
Given the importance of the RT to the methods of the paper, and the weight being placed on the novelty of the RT being used in this context, I would recommend revisions errors. Double precision float is required for treating a large number of voxel data (~1×10 9 points) whose values range from extremely small numbers to extremely large numbers.

[Answer to Minor Comment #2-2]
We thank the reviewer for the comment pointing out our error. We forgot to change the description in the premature version of the manuscript. Deconvolution was applied to "all" 3D images. We We thank the reviewer for the valuable comments for improvement of the paper.
According to the reviewer's suggestion, in the revised version, we described and reviewed the theoretical foundations on the Riesz transform and its applications with citing these articles. The sections of Introduction, Results, Discussion and Supplementary Notes were modified as follows in the revised manuscript: Introduction: Page 4, Line 68: "To overcome this problem, many methods have been developed to date (Shribak, Larkin et al. 2017). One of the most efficient and convenient methods adopts acquisition of multiple phase gradient images with orthogonal shears and their integration by Riesz transform (RT) (Arnison, Larkin et al. 2004, Larkin and Fletcher 2014, Shribak, Larkin et al. 2017. RT(Felsberg and Sommer 2001), which was independently and simultaneously proposed as the spiral phase transform , is a multidimensional extension of the 1D Hilbert transform (HT), and has recently been used in many fields of image processing and analysis , Unser and Van De Ville 2009, Bernstein, Bouchot et al. 2013, Püspöki, Storath et al. 2016.
These restoration methods with multiple DIC images precisely restore original images, but they require special equipment and multi-shot image acquisition that is disadvantageous for fast 3D live imaging. A method for single-shot DIC imaging with