Force inference predicts local and tissue-scale stress patterns in epithelia

Background

Embryo morphogenesis is inherently a mechanical process, where tissues fold, bend, loop and involute to reach their final geometries. In this regard, several techniques such as micropipette aspiration, magnetic tweezers and droplet injection have been developed in the last few years to probe the mechanics of epithelial tissues¹. However, these techniques are generally invasive to the sample being investigated and are laborious to perform. There is an urgent need therefore to develop non-invasive methodologies to study tissue mechanics. The force inference method provides a good alternative to obtain relative estimates of stress distribution in a tissue in a non-invasive fashion.

The force inference method² exploits the idea that at mechanical equilibrium, cell shapes are determined by a balance of contact forces between cells. Therefore, if cell shapes can be precisely determined by imaging followed by image segmentation, this method can be used for inferring relative tensions in a tissue. In the highlighted manuscript, the authors validate the force inference method numerically as well as experimentally by performing laser ablation in Drosophila tissues. They demonstrate the robustness of the force inference methodology in predicting stress patterns from single cell to tissue length scales.

Key findings

The authors first validated the force inference method, by generating in silico tissues using the Surface Evolver software. A classical vertex model was used to generate a user defined surface, where tensions at the edges of cells and pressures in cells were assigned a pre-determined value. Based on these values, the software then performs energy minimization of the surface to yield a final geometry. From the final geometry, cell shapes were determined following which the force inference method was used to infer forces in the energy minimized surface. The authors find an excellent agreement between the pre-determined tension/pressure maps and the distribution of forces determined by the force inference method.

The authors then proceed to compare the force inference method with laser ablation experiments performed in three different Drosophila tissues at different length scales. Single junctional tension was probed in the pupal notum, changes in tension across a small group of cells was analyzed in the ommatidia (four cone cells are present in a single ommatidium) and large-scale tension in a tissue across hundreds of cells was evaluated in the germband. For the ommatidia and germband case studies, mutant conditions were also tested. In each case, laser ablation was performed and the associated recoil velocity upon ablation was measured. The recoil velocity is proportional to the tension in the region of interest prior to the ablation. In addition, the force inference method was used to infer tension in the three tissues. The inferred tension and measured recoil velocity were highly correlated in each of the three cases suggesting that the force inference method provides robust relative estimates of stress patterns in a developing tissue.

Why I chose this preprint?

The biggest advantage of the force inference method is that it is non-invasive. It still relies on various assumptions in the different models used for force inference. However, it provides a good complementary approach to invasive methodologies and allows researchers to infer forces in hard-to-access tissues that are deep inside embryos. Moreover, the methodology allows force inference across different length scales – from cell level dynamics to tissue-scale morphogenesis.

Open questions

1. A pre-requisite for using the force inference method involves precise segmentation of the tissue of interest. The tissues chosen in this article are relatively easy to segment given the high contrast of the fluorescence signal. How should one proceed with using the force inference method for tissues where segmentation is noisy and error-prone?
2. A major assumption in the method that allows for inferring forces is that tissues are at mechanical equilibrium. However, this is not the case in many contexts of tissue morphogenesis, where cells undergo dynamic shape changes. What criteria can be used to determine when not to use the force inference method?

References

1. Sugimura K, Lenne P-F and Graner F, Measuring forces and stresses in situ in living tissues, Development, 2016.
2. Ishihara S and Sugimura K, Bayesian inference of force dynamics during morphogenesis, Journal of Theoretical Biology, 2012.

Tags: contractility, fly, force balance, material properties, tension

doi: https://doi.org/10.1242/prelights.7585

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