Effective mechanical potential of cell–cell interaction explains three-dimensional morphologies during early embryogenesis
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Curated by eLife
Evaluation Summary:
In this manuscript, effective force-distance curves between cells are inferred for various tissues. This study is potentially interesting for researchers interested in tissue dynamics, because computer models of growing cellular tissues are becoming an increasingly important tool to understand experimental data and eventually predict medical interventions.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. The reviewers remained anonymous to the authors.)
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Abstract
Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell–cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell–cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell–cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell–cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell–cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.
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Evaluation Summary:
In this manuscript, effective force-distance curves between cells are inferred for various tissues. This study is potentially interesting for researchers interested in tissue dynamics, because computer models of growing cellular tissues are becoming an increasingly important tool to understand experimental data and eventually predict medical interventions.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. The reviewers remained anonymous to the authors.)
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Reviewer #1 (Public Review):
Motivated by particle-based modeling approaches for describing tissue dynamics, the authors infer force-distance curves between cells in tissues from C. elegans, mouse embryos and MDCK cells. Each cell is represented by a point particle that interacts with all other cells via central body forces. The forces between cells are inferred via a data assimilation approach. From these data, average force-distance curves are obtained. They typically show a repulsive reign for particle distances smaller than the cell diameter and a short-ranged attractive region beyond the cell diameter. In particle-based simulations using these force-distance curves essential features of the tissues - including the stable formation of cavities - are reproduced. However, according to the force-distance curves cells can also interact …
Reviewer #1 (Public Review):
Motivated by particle-based modeling approaches for describing tissue dynamics, the authors infer force-distance curves between cells in tissues from C. elegans, mouse embryos and MDCK cells. Each cell is represented by a point particle that interacts with all other cells via central body forces. The forces between cells are inferred via a data assimilation approach. From these data, average force-distance curves are obtained. They typically show a repulsive reign for particle distances smaller than the cell diameter and a short-ranged attractive region beyond the cell diameter. In particle-based simulations using these force-distance curves essential features of the tissues - including the stable formation of cavities - are reproduced. However, according to the force-distance curves cells can also interact when they are not in direct contact in the biological samples. The authors denote these effects as 'indirect interactions through external factors'.
Although it is interesting to obtain measured forecasts-distance curves for use in simulations, a number of features remain problematic: Whereas the assumption of central body forces might be appropriate for bulk tissues, it is not the case for tissues with cavities. There, the interactions between adjacent cells in contact with each other are different from those with 'indirect interactions'. It is unclear what one learns in this case from the effective average force between cells. Furthermore, the data exhibit large variations in the inferred force between cells at a given distance. These variations can be a multiple of the average value and, for a given distance, the distribution of forces spreads on a wide range of positive and negative values, i.e., are repulsive and attractive. The force-distance curves change with time. Is this only a consequence of cell growth or are cell properties changing? Finally, the authors do not study the robustness of their results against variations of the force-distance curves. In Fig. S12 they show that forces derived from the Lennard-Jones or a 'freehand' potential yield qualitatively similar results in most situations.
In conclusion, even though simulations using the inferred force-distance curves may yield structures that are similar to those found experimentally, it remains insufficiently clear what biological insight is gained in this way.
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Reviewer #2 (Public Review):
Growth is an essential property of life but is in itself an intrinsically mechanical process to understanding the mechanical effects of growth computer models of growing tissues have been derived and help to understand and interpret experimental data and mechanical effects in growing tissues. In this work, the authors optimize effective cellular interaction potentials to best reproduce cellular displacements in experimental studies. Growth is unfortunately not taken into account. Nevertheless, this work can help contribute towards developing accurate and predictive in silico tools for growing tissues.
A limitation lies in the assumptions. The authors demonstrate that their method correctly identifies the interactions from simulated cells with given interaction potentials and thermal noise. However, cells do …
Reviewer #2 (Public Review):
Growth is an essential property of life but is in itself an intrinsically mechanical process to understanding the mechanical effects of growth computer models of growing tissues have been derived and help to understand and interpret experimental data and mechanical effects in growing tissues. In this work, the authors optimize effective cellular interaction potentials to best reproduce cellular displacements in experimental studies. Growth is unfortunately not taken into account. Nevertheless, this work can help contribute towards developing accurate and predictive in silico tools for growing tissues.
A limitation lies in the assumptions. The authors demonstrate that their method correctly identifies the interactions from simulated cells with given interaction potentials and thermal noise. However, cells do not necessarily interact with conservative pairwise forces. Interaction potentials can only be an approximation that describes the tissues behavior in certain limits.
The content and structure of this manuscript could be improved. In particular, it is difficult to judge how well the method works.
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