Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy

Sacha Ichbiah, Fabrice Delbary, Alex McDougall, Rémi Dumollard, Hervé Turlier

Preprint posted on 13 April 2023

May the (3D map of the) force be with you, and guide you through the labyrinth of embryonic development

Selected by Girish Kale


Imagine you have a balloon in your hands. Can you guess whether it is under a lot of pressure? Probably yes, right? We might even be able to do this blindfolded, but we can’t really guess the pressure if someone just shows us a picture of the balloon. One way to guess the pressure could be by using a slow-motion video of the balloon as it bursts. As we can imagine, balloons under greater pressure would likely burst more violently. But obviously then the balloon is gone, and all the fun it might bring.

At a certain level of simplification, cells are a bit like balloons filled with water (or honey, if we allow some additional level of complexity). Now the question is, can you guess the surface tension and pressure in a cell if someone shows an image of it to you? How about when a bunch of cells are clumped together, undergoing the complex biological processes of embryo development? Also, if possible, this guesswork better not involve bursting cells; after all, cells are the basis of life and we would like to preserve them, and pick non-invasive methods as much as possible. As it turns out, such guesswork is possible using computational methods that fall under the umbrella term: force inference methods.

As the name might suggest, force inference methods can infer tissue-scale forces, at sub-cellular resolution, from an image of the cell boundaries. Typically, such inference works under several assumptions about cell/tissue mechanical properties. And although the inference has its limitations, it still provides insights about cell behavior and helps predict tissue-scale deformation to follow. Unfortunately, a major caveat with current inference methods is that they work well in 2 dimensions, but not so well when the 3rd dimension needs to be accounted for. The preprint I’ve picked here is trying to address this gap by establishing a force inference method that would work well for 3D structures, such as embryos from various species.

Key findings:

As usual, the authors needed good quality images showing the cell boundaries, and then a good ‘segmentation’ of these images, to generate the data that could be fed into the computational pipeline. The authors realized that current image segmentation methods were inadequate for this purpose, and thus first decided to improve these methods to fruitfully identify cell surfaces. This step is crucial: the segmented cell surfaces are approximated with a triangular mesh, and the straightness of cell contacts and the curvature of the cell surfaces are key inputs that allow the measurement of the mechanical parameters. Going back to the balloon analogy, imagine being shown a picture of balloons pressed against each other, and being asked which balloon has greater pressure. It is possible to solve this riddle, since the balloon with lower pressure will have a greater indentation. As we can imagine, the quality of the picture of the balloons will limit our ability to estimate the relative pressures.

After improving image segmentation, the authors performed a nuanced and extensive benchmarking of their computational pipeline. This involved trying out different variants of the mechanical models to test their sensitivity to the noise in the input data, using these models to generate embryos with a few cells in silico, and comparing them with images of real embryos. After this benchmarking exercise, the authors applied their methods to understand the mechanics of embryos from 3 different species: mouse (mus musculus), sea squirt (Phallusia mammillata), and roundworm (Caenorhabditis elegans). This covers a wide diversity of embryo sizes (40-200 μm), embryo shapes (round vs. elongated), embryo structures (enclosed in a shell vs. free), and developmental processes. Interestingly, the authors could use their model to predict cell/tissue behavior, and demonstrate the similarities between their predictions and expected cell/tissue behavior known from previous studies.

Importance of the findings:

Various studies so far have implemented invasive methods to gauge the mechanical properties of cells and tissues, all of which have their own drawbacks. For instance, laser ablation has been used to estimate tension between neighboring cells, but is applicable mainly when the stiffness is low. Micropipette aspiration can only access the cell-medium interface, so surface tension at internal cryptic surfaces is not accessible. Also, this method can’t be easily implemented in embryos that have an outer shell, and thus has been used to measure the surface tension only in free floating embryos. Further, the applicability of these methods might change depending on the size of the probed structures: laser ablations might be difficult to achieve if the cell contacts are short, while micropipette aspiration would be complicated for small cells. More importantly, the invasive methods are perturbing the normal development of the embryos, no matter how subtle the perturbation might be. The authors here demonstrate that their non-invasive method works in differently sized embryos with a variety of cell sizes.

It is also important to highlight improvements accomplished in this manuscript, as it successfully implements force inference in the 3rd dimension as well. Not only that, but according to the authors the same methods would still work well in 2 dimensional scenarios. With the codes being written in python, the method is now freely available to all cell/tissue mechanics aficionados.

Questions to authors:

1) The force inference pipeline seems to work beautifully in embryos during early stages of development, when there are few cells. How challenging would it be to apply it during later stages of development when there are many cells? Will segmentation be the bottleneck, or the computational complexity due to increasing number of components?

2) The 3D structure of the tissue is important. But many processes have been analyzed in 2 dimensions with great success. For instance, in Drosophila embryos, the 2D force inference has been applied in convergent-extension movements in the ectoderm, or the invagination of the mesoderm. Do you think a 3D analysis holds answers to questions that haven’t been addressed yet, or that may not even have been asked yet?

3) How easy would it be to apply your force inference methodology to organoids? Could this provide a way to predict, in real time, if an organoid is on the right trajectory to form the desired differentiated organ?

Tags: early embryonic development, fluorescence microscopy, force inference methods, image analysis, mouse, roundworm, sea squirt

Posted on: 4 May 2023


Read preprint (No Ratings Yet)

Author's response

Hervé Turlier shared

1) The limitation of the method lies indeed mainly in the quality of the imagery as suggested by the question, which will determine the quality of the segmentation, the reconstruction of the mesh and the measurement of the geometric characteristics. And the image quality will necessarily decrease if the number of cells increases at the same image size. The limitation isn’t really in scaling the mesh method and inference calculations to larger tissues (although we haven’t studied this scaling behavior extensively). Nevertheless, the computation time will increase notably with the number of meshes and/or the precision of the mesh if one wants to extract the pressures of the meshes with our new formulation of balance of pressure known as “variational of Laplace”, which is more expensive in calculation than the direct measurement of the mean curvature of the interfaces to invert Laplace’s law. The calculations have not been parallelized (on the GPU for example), but this could be a future evolution of our code, depending on the needs of the community as well as ours.

2) Yes, we believe that the possibility of accessing the 3rd dimension in terms of cell mechanics will trigger new questions that have not yet been asked or still deserve detailed mechanical characterization, such as internalization or cell extrusion or cell sorting. With respect to epithelia specifically, the role of line tensions remains largely uncharacterized in 3D: tensions inferred in 2D from the apical side of epithelia are in fact line tensions located at tricellular junctions in 3D, which scale differently than surface tension. So far, our method is not accurate enough to also infer line tensions, so in this case more effort will be needed to accurately link 2D and 3D inference and to characterize the relative roles of line and surface tensions. For non-epithelial cells in organoids, we believe that our method may be readily tested.

3) We hope that the inference method will also be useful for predicting 3D mechanical maps of organoids and tissues. The relevance of the deduced forces will however depend on the adequacy of the shape of the cells to the underlying mechanical hypothesis of the foam, expressed by the Young-Dupré and Laplace force balances. This hypothesis seems reasonable at the early stages of embryo development: it is interesting to note that 3D force inference appears to be the only tool available – to date – to assess precisely on 3D cellular structures the true relevance of this physical analogy, which was proposed over a century ago by D’Arcy Thompson. At later stages of development, specialized cells may acquire more complex shapes that do not conform to this physical model; extracellular components such as the matrix or surrounding tissues may become mechanically important, and the nucleus, of vastly different mechanics, may be compressed and may dominate the mechanical response of the tissues. The foam hypothesis is therefore a starting point for 3D mechanical inference methods, but it will soon have to be revisited to take into account more complex environments and mechanical constraints. The use of force inference for real-time mechanical prediction, with potential feedback to guide the morphogenesis of developing organoids, is a very attractive idea. Note, however, two limits of current force inference methods: 1) the question of the temporal calibration of static mechanical maps has not yet received a generic technical answer (in 2D, we have just demonstrated the feasibility of calibrating the inferred maps over time using myosin fluorescence as an indicator of tension in the C. elegans embryo); 2) if development is fast (timescales of minutes), the entire pipeline (segmentation, mesh creation, inference) may need to be parallelized on GPU to be fast enough for live use.

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