Unified quantitative characterization of epithelial tissue development

Please try to revise the writing to make it less technical and more accessible to broad biological audience. The impact of the paper could be greatly increased by predicting and validating the morphogenetic outcome of perturbing a specific cellular process. Please consider if this is within the scope of the present manuscript, and if not, relate to it in the writing.

We thank you and the referees for constructive comments that helped us improve the quality of our manuscript. As requested, we have substantially modified the manuscript to improve its impact and general relevance as follows:

i) For biologists, we have edited the main text and the figures to make the manuscript more accessible to a broad audience: (a) we have removed or replaced mathematical and technical terms; (b) as requested by reviewer 3, we have provided three additional or improved schematics to better explain how tissue growth and morphogenesis is measured (Figure 1A; Figure 1–figure supplement 1A; Figure 1D), how the formalism is implemented in practice (Figure 1E and Video 1) and how the role of each cell process is measured (Figure 4C). For physicists, we have significantly improved the appendix by providing a more comprehensive and detailed description of the formalism, its principle and implications.

ii) As suggested by reviewer 2, we have applied the formalism to another epithelial tissue (Figure 5 and Figure 5—figure supplement 1; Video 5). By analyzing a time-lapse movie corresponding to ~2 10⁶ cell contours, we have performed a complete analysis of the wing pupal development during 17 hours. This analysis improves the generality of our works since:

The pupal wing is an important model to study epithelial tissue morphogenesis, this novel dataset and its analysis is therefore of general relevance for the study of tissue morphogenesis.

In our initial version, by analyzing the notum pupal epithelial tissue we described and quantified an unexpected case of interplay between cell division orientation and tissue elongation where cell division is orthogonal to the overall tissue elongation (Figure 4B, E). In the revised version we have demonstrated that this interplay is also present in the central region of the wing (Figure 5C, G). This therefore reinforces the generality of our initial findings.

iii) As requested, we aimed at perturbing a cellular process to illustrate how the formalism can be used to analyze the role of cell processes during epithelial tissue morphogenesis (Figure 6 and Figure 6—figure supplement 1). To this end, we have recorded the morphogenesis of five mutant tissues where the tribbles gene (an inhibitor of G2/M transition) is overexpressed to block cell division (trbl^up tissue). This dataset of ~3.7 10⁶ cell contours has been fully segmented and analyzed and has yielded novel results important for the field of tissue development:

In trbl^up tissue, both visual inspection and cell tracking revealed a drastic reduction of the number of cell divisions (4.3% of the number in the wild-type tissue). As expected we found that the convergence-elongation rate of division measured by the formalism nearly vanished.

To go beyond this expected prediction and to analyze in more detail the role of cell division and its interplay with other cell processes, we have then developed a complete set of general methods to compare wild-type and mutant conditions (“Comparisons of wild-type and mutant conditions”). Applying these methods to our experimental dataset demonstrates that both cell proliferation and cell division orientation are critical to promote tissue elongation and furthermore that cell divisions indirectly impact both cell rearrangements and cell shape changes.

To further analyze and better understand these experimental findings, we have performed additional computer simulations. As observed in the experimental dataset, the computer simulations show how cell divisions can promote tissue elongation regardless of their orientation by indirectly influencing both cell rearrangements and cell shape changes during tissue elongation (Figure 6K-M).

Altogether, the above additional results from experiments and computer simulations illustrate that our formalism enables to study quantitatively tissue morphogenesis and to uncover complex interplays between cell divisions, cell rearrangements and cell shape changes by quantifying tissue dynamics in wild-type and mutant tissues and by allowing the comparison between experimental and simulated datasets.

In conclusion we have fully addressed all the reviewers' comments: (i) by editing the manuscript to make it more accessible to biologists and by adding schematics to better explain its technical aspects; (ii) by applying the formalism to another epithelial tissue; and (iii) by analyzing a mutant condition and computer simulations to illustrate the relevance of the formalism in the study of epithelial tissue morphogenesis. We therefore hope the manuscript will now be deemed suitable for publication.

Reviewer #1:

[…] I just have the following questions before recommending the paper for publication: 1) If cell rearrangement also happens via higher order intercalations (5-fold vertices or higher), how would this additive model account for the various order of intercalations, are they simply additive? I.e. R=R(4)+R(5)+…?

Yes, one of the strong points of the formalism is that it allows to take into account and sum up all cell processes. This includes decomposing the total contribution of rearrangements into its different types.

We have clarified this point by stating in the main text: “Whenever needed, the subdivision of these main cell processes can be further refined, for instance in a mono-layered tissue to distinguish apoptoses from live cell extrusions, or to distinguish simple rearrangements through 4-fold vertices from those with 5-fold vertices or higher.” We have also detailed in the appendix how such a decomposition could be performed.

2) Can the formalism be applied in the presence of cell-substrate interactions in addition to cell-cell interactions, such as when cells are self-propelled?

Yes, the formalism uses cell contours and cell lineages to quantify tissue morphogenesis. This approach, which delivers important and quantitative information on tissue development, is purely descriptive and independent of the forces that give rise to this morphogenesis. It can therefore be applied whether in presence or in absence of cell substrate interaction, to describe the respective contribution of each morphogenetic process to tissue deformation.

We now state in the appendix that “our formalism for deformable cellular materials quantifies observed morphogenetic changes independently of the biological or physical origin of the forces that drive these changes, whether internal forces such as active cytoskeletal forces, viscous dissipation or cytoplasm pressure, or external forces such as interaction with another cell layer or solid substrate.”

In addition, the force inference method used to estimate the junctional stress (i.e.the stress transmitted at cell junctions) is independent of other contributions to stress or of external force contributions; it thus remains valid even in the presence of cell-substrate interactions that can cause an additional contribution to the total mechanical interactions.

We now state in the Materials and methods (Force and stress inference): "Junctions contribute to transmit stress between cells even if the biological origin of this stress lies in non-junctional cytoskeletal elements and other structures in the body of the cell. Forces created in the cell body or at the cell boundary are transmitted to its neighbours by contact at the cell-cell interface. These forces transmitted by contact can be decomposed in components parallel and perpendicular to the junction, namely tension and pressure, which we both estimate. Changes of cell volume lead to measurable changes in pressure and thus to detectable changes in our stress estimation."

3) I think the method here requires the tissue to be confluent? Is the texture tensor a good quantity to use when there are holes in the tissue or there are boundaries involved?

The formalism is constructed rigorously to take into account all links between cells, and all their possible changes, whether these cells are at the tissue boundary or not. It thus applies to tissues with boundaries, even with internal ones like in the case of actual holes in the tissue, or in the case of holes in the skeletonized images due to segmentation problems.

We state in the manuscript appendix that describes in detail the formalism: “Note also that the formalism is meant to extract relevant information from cell-cell links, to apply to a confluent cell assembly. Still, J* systematically takes into account all links between cells at the tissue boundary, and all their possible changes. The formalism is thus designed to rigorously take into account all links between cells, and all their possible changes, whether these cells are at the tissue boundary or not. It applies to tissues with boundaries, even with internal ones like in the case of actual holes in the tissue, or in the case of holes in the skeletonized images due to segmentation problems.”.

Reviewer #2:

[…] Substantial concerns: The notion of the formalism itself is a bit obtuse for the average biologist and this should be clarified to make the main concepts more accessible.

We have improved the manuscript by making it more accessible to biologists: (i) by removing mathematical and technical terms (ii) by focusing on the four main epithelial processes: cell division, cell rearrangement, cell shape and size change and apoptosis; and (iii) by introducing or improving cartoon-like schemes to better explain the measurements of the formalism (Figure 1A, D and E; Figure 1—figure supplement 1A; Figure 4C). Importantly, an appendix now provides in-depth mathematical description of the formalism and its practical implementation.

The impact of the work would be greatly improved by demonstrating that genetic or biophysical disruption of the tissue (i.e. through gain/loss of function cell clones, mechanical injury, etc.) leads to predictable and reproducible changes in the various cell parameters under consideration. In other words, can the formalism be used to elucidate cell- and tissue-level implications of different genetic or mechanical perturbations? Similarly, can it be applied to other experimental systems/context? As it stands, the work nicely describes wild-type notum morphogenesis but it seems to me the impact of this methodology could be significantly extended.

We have fully addressed this point by (i) applying the formalism to another epithelial tissue: the Drosophila pupal wing (Figure 5; Figure 5—figure supplement 1; Video 5) and (ii) analyzing, using both mutant experimental data and computer simulations, the impact of a drastic reduction of the rate of cell division (Figure 6 and Figure 6—figure supplement 1). We have described in detail the important conclusions we could reach (please see detailed answer in the “Essential revisions” section above) and how these additional results improve the general relevance of our manuscript and provide a comprehensive set of methods to study tissue morphogenesis.

Reviewer #3:

[…] 1) The paper is mainly technical. As such, it will appeal to a relatively small community. There is no doubt that the method reported here has great potential but the current manuscript does not provide a fundamental advance in our understanding of biology (other than the distinct contributions of cell division to tissue growth). If technical papers like this one fall within the scope of eLife

then this paper provides an interesting formalism to systematically map tissue dynamics. Otherwise, I think specialized readers would prefer another type of manuscript integrating the main text and the supplement into a single body, and including a more detailed validation.

eLife guidelines to authors specifically encourage “Tools and Resources” papers. In addition, with respect to the initial version, the revised version has been significantly improved by the incorporation of additional validation, and additional results in the pupal wing and in mutant notum tissues. Finally, we have followed the editors’ recommendation to make the text more accessible to biologists.

2) Very important methodological aspects are missing or buried in the formalism of the supplementary materials. The main text should include additional details on how each contribution to the global growth rate is determined. For example, the reader is left wondering how the authors distinguish between cell apoptosis or delamination, or between cell division, inclusion of a new cell, and a cell rearrangement. In general the main text should be much more informative on the methods and, where possible, provide schemes and intuitive pictures to the non-expert reader.

We have addressed this point as follows:

To help the readers and as suggested by the reviewer (point 4), we have added schemes to better illustrate how each cell process is measured by changes in link between cells (Figure 1A and Figure 1—figure supplement 1A).

We have added a figure to illustrate that the formalism is applied after cell segmentation and cell tracking and lineage determination (Figure 1E); Furthermore, we have described in more detail how upon segmentation of the movie each process is distinguished by cell tracking and cell lineage determination prior to applying the formalism (Materials and methods, “Practical implementation of the formalism”).

We have revised our manuscript to make sure that all methodological and practical aspects are fully described in the text or the Materials and methods, while the appendix contains all technical explanations regarding the theoretical framework. We have followed the overall recommendation to make the main text more accessible to biologists.

Regarding delamination versus apoptosis, we explicitly state that in our movies, our segmentation and tracking methods do not distinguish between delamination associated with apoptosis or cell delamination without apoptosis (live cell extrusion). Distinguishing between the two types of delamination can only be done by introducing an additional marker such as Histone-mRFP to observe nuclear fragmentation. We have described in the appendix how delamination and apoptosis, if they were distinguished by image analysis, could be independently quantified by the formalism, if needed.

Importantly, all cell processes, which can be distinguished by analyzing cell contours, are characterized during the cell tracking and then rigorously quantified separately by our formalism to characterize their contribution to tissue development.

We state in the appendix: “the contribution of delaminations and apoptoses. If needed, this can be subdivided into sub-processes, each associated with a different biological origin, for instance to distinguish simple extrusions from extrusions associated to apoptoses; or apoptoses which occur for cells with 3, 4 or more sides. Their contributions naturally add up, by construction of our formalism.”

3) The validation of the method (Figure

2) is largely qualitative. The authors should first explain the types of errors the method is sensitive to, and then quantify those errors.

We have made our validations more quantitative. In the revised version, we have first validated G(tissue deformation) and S(cell shape and size changes) measurements by performing a simulation where a cell patch undergoes a known isotropic dilation followed by a known contraction-elongation along the x axis (Figure 2A, Video 2A). We then measured separately G and S(both dilation and CE rates), compared the measurements to the input deformation and found an error of 0.3%.

Having validated G, we then validated the measurements of D(divisions, Figure 2B and Video 2B), R (rearrangements, Figure 2C and Video 2C), and A(apoptoses, Figure 2D and Video 2D), with simulations involving almost exclusively those cellular processes (since some residual rearrangements and cell shape changes always occur in our simulations due to cell structure disorder). The analysis yields the balances G= D, G= Rand G= A, respectively (up to residual contributions of R and S), thereby validating D, Rand Ameasurements. As now detailed in the appendix, we have explained that the tissue deformation rate is independent of rigid body movements including rotation. This is illustrated and validated by performing additional computer simulations (Figure 1—figure supplement 1 D, E and Video 2H, I).

In the revised version, we have added a complete section in the Materials and methods (Uncertainties) where we now discuss more precisely the errors due to image analysis (segmentation and tracking), which affect the input of our formalism, as well as the approximations used in our description, which affect the output of our formalism.

4) The examples on Figure

1 are not very clear. In particular changes in size and shape in panels C, D, E are not visual. Perhaps a more schematic cartoon-like illustration would help.

As requested we have improved this figure by providing schematic cartoon-like illustrations to explicitly describe how changes in link geometry and topology can be used to quantify the four main cell processes (cell division, cell shape change, delamination and cell rearrangements, Figure 1A) as well as the other processes (Figure 1—figure supplement 1A).

5) Can the third dimension be really ignored? What is the error in the deformation rates caused by the assumption of a 2D tissue?

We image the tissue in 3D using the E-Cadherin:GFP marker, which labels the apical adherens junctions in Drosophila tissue. This permits to measure the tissue curvature of this cuboidal monolayer epithelial tissue. We have better emphasized that the corrections due to tissue curvature are small in the notum and entirely negligible in the wing.

We have mentioned in the Materials and methods (Uncertainties): "The 3D structure of the notum also plays a role because the tissue is curved. It is imaged in 3D using a confocal microscope; the height of its surface is recorded and we can entirely reconstruct its curvature. […] For simplicity, we choose not to perform any correction to our results, knowing that we can perform the correction a posteriori if it appears necessary in the future. All these effects are completely negligible in the wing, which is much flatter than the notum.”

6) In the quantification of the force field the authors assume the junctions are the sole structures responsible for stress transmission. However, the cell body is likely to contribute to the generation of active stresses through, for example, changes in cell volume (see Saias et al., Dev Cell 2015) or non-junctional cytoskeletal elements. This should be critically addressed.

In the revised version, we clarify that what we measure is the junctional stress (Materials and methods, Force and stress inference). Junctions contribute to transmit stress from cell to cell even if the biological origin of this stress lies in non-junctional cytoskeletal elements and other structures in the body of the cell. As we explicitly state, forces created in the body of a cell or at its boundary are transmitted to its neighbors through contact forces at the junction, which can be decomposed in components parallel and perpendicular to the junction, namely tension and pressure, which we both estimate (Figure 7—figure supplement 1). Changes of cell volume (such as observed by Saias et al., Dev Cell 2015) lead to measurable changes in pressure and thus to detectable changes in our measurements.

We agree that junctional stress can differ from the total stress in some cases, and that junctions are not the sole structures responsible for stress transmission. We explicitly state that there can be contributions that we do not measure in the total stress (Materials and methods, Force and stress inference): “Note that we cannot measure other contributions to the total stress, for instance through cell membrane parts far from adherens junctions.” Our work focuses on junctional stress because of the growing consensus that junctional stress is an important determinant of tissue morphogenesis as measured by laser ablations of (and outside of) adherens junctions (for review Lecuit et al., Annu Rev Cell Dev Biol, 2011), or directly probed by experimental manipulation of adherens junctions and compared with simulations (Bambardekar et al., PNAS 2015).

7) The finding that cell division can lead to positive or negative growth is intriguing but very preliminary. The authors should at least provide some images of the tissue illustrating the mechanisms underlying the two opposite behaviors. A cartoon would also help.

In the revised version, we now clarify that division can only contribute positively to growth, in the sense that the isotropic part of the division tensor Dis always positive, thereby always having a positive effect on local tissue growth in term of area increase (Figure 3—figure supplement 1B).

In the present article we focus on the anisotropic parts of tensors, which correspond to contraction-elongations that do not change the local tissue area and impact tissue morphogenesis. To address the reviewer comment we have improved our manuscript as follows:

We have rephrased the definition of the projection of each cell process measurement along the total tissue CE rate (G). To avoid any confusion, we now call it “component along G”. We have also included a figure panel to explain more precisely the meaning of a negative versus positive component of each cell process (Figure 4C). A negative component of Dsimply results from cell divisions mainly oriented orthogonally to tissue elongation.

We have performed additional simulations of cell divisions oriented orthogonally to the main direction of tissue elongation, illustrating the case of a negative component of cell division along tissue elongation (Figure 6K-M). This illustrates the mechanisms underlying the two opposite cell division behaviors: aligned with versus orthogonal to tissue elongation.

To reinforce the general relevance of our initial findings on cell division, we have firstly performed a complete analysis of wing morphogenesis (Figure 5 and Figure 5—figure supplement 1; Video 5). This analysis shows that divisions are found orthogonal to the main direction of tissue elongation in this tissue too. We have secondly undertaken an in-depth analysis of the role of cell divisions. This was achieved by overexpressing the tribbles gene to prevent cell proliferation, analyzing using the formalism five tribbles overexpressing tissues (Figure 6 and Figure 6—figure supplement 1), defining a complete set of methods to rigorously compare wild-type and mutant conditions, and using both experimental and simulation data to analyze a complete analysis of cell division contribution to morphogenesis (please see detailed answer in the “Essential revisions” section above). We have therefore validated that the formalism allows comprehensive and novel studies of cell processes during tissue morphogenesis.