Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density

Changes in tissue geometry during developmental processes are associated with collective migration of cells. Recent experimental and numerical results suggest that these changes could leverage on the coexistence of nematic and hexatic orientational order at different length scales. How this multiscale organization is affected by the material properties of the cells and their substrate is presently unknown. In this study, we address these questions in monolayers of Madin-Darby canine kidney cells having various cell densities and molecular repertoires. At small length scales, confluent monolayers are characterized by a prominent hexatic order, independent of the presence of E-cadherin, monolayer density, and underlying substrate stiffness. However, all three properties affect the meso-scale tissue organization. The length scale at which hexatic order transits to nematic order, the “hexanematic” crossover scale, strongly depends on cell-cell adhesions and correlates with monolayer density. Our study demonstrates how epithelial organization is affected by mechanical properties, and provides a robust description of tissue organization during developmental processes.

1.The manuscript is, in its current form, somewhat difficult to follow.In order to improve the readablilty, I would propose that a theoretical scheme showing the main theoretical concepts is needed.In Fig. 1, for example, a scheme of what does it mean to ask for the order in the different rotational-symmetry based indexes is necessary.In addition, a scheme of what is a cross-over between hexanematic and 2-nematic order would be very useful.With that, the reader who is not specialist with the exact methods proposed in the manuscript can have an idea of what phenomenon is presented.
2. I guess in all the manuscript the assumption of confluence is at work, although this is sometimes not totally clear.In addition, increasing/decreasing density seems to be a key factor throughout all the discussions.Does it imply that cells can be compressed?On the contrary, reduction of the density may lead the tissue in tension.How does this affect the results?In a low density tissue, where, according to the authors, 2-nematic order seems to be more pronounced, can the authors rule out any external tension?Is it related to the surface stiffness?Please clarify this point.
4. The paper is built upon the theoretical analysis provided in refs.30 and 31.In the manuscript the theoretical approach is porrly explained.Please enlarge the supplementay material such that the paper is better self-contained.Please, frame better the different elements involved.In addition, the current version seems to have some mistakes.In particular, in the supplementary material: •Equation 1: State that "V" is the number of vertices of the 2D polygon •Equation 1: State that "p" is the rotational symemtry considered •Line 4 after equation 1: The definition of r_c has a mistake, as the maximum value of the sum index should be "V" instead of "N" •Equation 2: Specify what the index _c is --i.e., the c-th cell.
•Is N different from N_R? 5.In the statistics, there is a constant use of the p-value.For example, in page 3, 1st column, line 24, it is stated that the mean ± sd of the cell index has a p-value <0.00001.Why do you need the p-value here?Considering that the sd is lower than an order of magnitude of the mean, I think there are no reasons to consider that it the mean ± sd is not valid enough?Against which nullmodel is the p-value computed?I may misunderstand something here so, please, clearify this point.
6. Ref. 30 seems to touch quite similar topics and reaches similar results, with some of the authors also being in the author list of the manuscript under revision.The presence of overlap is not a priori a problem, please clarify what is new in this submition.
7. There are some typos in the text, hence it should be thoroughly checked.
I may better appreciate the depth of the results provided in the paper if I read a revised version of it, which I will be pleased to do.Anyway, I feel the paper has potential enough to be published in Natcomms.
Reviewer #2 (Remarks to the Author): Mechanisms of cell collective motion in biological tissues depend on the length scale on which motion is considered.Since different kinds of cell ordering prevail at different scales, hexatic at smaller and nematic at larger scales, it results that local order and collective motion mechanisms are strictly related.Tissues dynamics is very relevant in many biological processes, therefore it is important to study the behavior of the hexatic-nematic crossover length and its dependence on different system parameters.Hexatic and nematic order with its crossover are experimentally studied in this article for different systems.
It is demonstrated that the hexanematic crossover shifts towards shorter length scales for decreasing monolayer density and reduction of the cell-cell interaction.This is a central result well demonstrated in this study that I believe noteworthy for the research community in this field and for more general biological implications.The experimental methodology and data analysis well support the conclusions presented.The paper is written in a very clear way.I recommend the publication of this work in its present form.

Manuscript Title: Hexanematic crossover in epithelial monolayers depends on cell adhesion and dell density
We thank both reviewers for taking the time to review the manuscript and for their insightful comments.We have incorporated changes in the manuscript to address the suggestions made by the reviewers.Responses to the reviewers' comments can be found point-by-point in the text below.All changes in the manuscript are highlighted red.
Reply to Reviewer #1 )(8'$,2/272.2-<$2;$0(10'(.<$'D0.)2+'59$Reply: We thank Reviewer #1 for communicating the concerns regarding the clarity of our manuscript.To improve we revised parts of the content based on the comments raised.We hope that the improved version further clarifies our message, and by this can be appreciated by a broader audience.See the text in red for our changes.$ 3)-24$)+5$GB+'3)-24$1(5'($A16.5$7'$,'(<$6/';6.9$:2 Reply: The revised version of the manuscript includes a whole new figure, Fig. 1, where we have illustrated the concept of multiscale order as well as that of hexanematic crossover at a more intuitive level.In addition to this, we have substantially expanded the introduction, to explain the relevance of this fascinating form of spatial organisation in tissues, and the methods section and Fig. 3 (previously Fig. 2), to provide the readers with a precise and pedagogical account of how the various quantities are computed.
6(;)4'$/-2;;+'//J$M.')/'$4.)(2;<$-&2/$012+-9$Reply: Experimentally, we seeded cells at different starting concentrations on coverslips.After seeding, epithelial cells will (within limits) cover all area available to them.Thus, different seeding concentrations naturally result in different cell densities (cells per area).Cells at lower densities tend to be more elongated than cells at higher densities, see Refs ( 19) and (42) in the manuscript.These density variations affect, for example, the cortical tension and traction forces of cells.In our manuscript, we capture the impact of density variations on the tissue's symmetry.
As Reviewer #1 notices, varying the cell density does affect the stress distribution of the monolayer.However, as the latter is not laterally confined, such an effect is not the same that would result from an externally applied lateral compression or extension of the entire cell monolayer.Conversely, all stresses at play in the monolayer are internally generated, with only exception for the hydrostatic pressure resulting from the fluid in which the monolayer is embedded.Being stress an extensive quantity, the larger the number of cells pulling (as a result of contractility) and pushing (as a result of motility) on each other, the larger the local stress.Now, as some of us theoretically predicted in Ref.
[31], increasing the active stress at the cellular scale results in an increase of the crossover scale !!, thereby extending the range of length scales at which hexatic order prevails over nematic order.Our observations confirms this predictions.It should be noticed that, whether at low or high density, our cell monolayers never experience a +'-extensile stress, as this would result in breakdown of confluency, which, instead, it is never observed.By contrast, and consistently with Ref.
[41] (Saraswathibhatla and Notbohm, Phys.Rev. X 2020), increasing cell density decreases the alignment among stress fibers, thus further strengthening hexatic order.Analogously, decreasing density increases the alignment of the stress fibers, thereby enhancing the unidirectional stresses form which nematic order originates.We have elaborated on these concepts at the end of the section "Hexatic order strengthen with the monolayer density".
Finally, as Reviewer #1 suggests, cellular contractility is counterbalanced, at least in part, by the substrate.For this reason experiments were performed for a range of substrate stiffnesses (see "Lower substrate stiffnesses reinforce the length scale of the hexatic order driven by cell-matrix and cell-cell adhesions").Our findings indicate that unidirectional cellular contractility increases with substrate stiffness, thus leading to the shift of the hexanematic crossover towards smaller length scales.
Reviewer #1 (Remarks to the Author): The revised version of the mansuctipt "Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density" addressed successfully comments.The responses of the authors to my comments were also satisfactory.I spotted a small typo in equation ( 2): It should read N_cell instead of N_cells, if one wants to be in agreement with the definitions.I thereby recommend the manuscript for publication.