Role of intercellular adhesion in modulating tissue fluidity

Reviewer #1 (Public review):

Summary:

The manuscript by Ray et al. provides a theoretical framework to study tissue mechanics and the solid-to-fluid transition phenomenon observed in many tissues. The authors advanced previous models by directly incorporating cell-cell adhesion in force calculation with flexible cell geometries. They performed an in-depth analysis of the model and found that reducing cell-cell adhesion in near-confluent tissues can result in spontaneous cell rearrangements and transition to tissue fluidity. This is in contrast with previous predictions of Vertex models, which require higher adhesion for solid-to-fluid transition.

Strengths:

The authors provided a more general formulation of a 2D active foam model by directly incorporating cell-cell adhesion and performed a careful analysis of cell dynamics and cell shape in their simulations. They measured various quantities such as the mean-squared displacement of the cell center and shape index, which was introduced in previous studies to analyze jamming transition in tissues. By careful analysis of their simulations, they found a universal length scale in their simulations, explaining the observed heterogeneity. They provided a qualitative connection to previous experimental observations, where a reduction in cell adhesion caused tissue fluidity.

Weaknesses:

The phenomenon of tissue fluidity is an important and open question in biology. While theoretical models provide guidance to study such complex phenomena, the details in these models should go hand-in-hand with quantitative comparison with experiments. The study by Ray et al. indeed provided a more detailed description of deformable and adhesive cell collectives, but without a quantitative comparison with experiment, it is not clear if one needs all these details, or maybe more is needed. For example, do we need a more detailed mechanical model of the vertices, how the friction with substrate should be incorporated in such models, and is there a feedback between cell dynamics and its internal cytoskeleton organization?

While the manuscript by Ray et al. is an interesting theoretical study, without a quantitative comparison with experiments, it is not clear if it truly advances our understanding of tissue mechanics.

Reviewer #2 (Public review):

Summary:

Ray and coworkers introduce a discrete model of cellular layers aimed at investigating the role of inter-cellular adhesion in collective cell migration. The model combines aspects of particle-based models, in which cells are treated as simple point-particles with pair-interactions, and "morphological models", where interactions primarily depend on the cellular shape. In this case, cells are modeled as rings of beads connected by springs, thus allowing for exploration of the role of cell morphology while treating intercellular interactions as particle-like. Upon exploring the parameter space of this model, the authors recover physical behaviors reminiscent of reconstituted cell layers, including the onset of collective cell migration, when the forces leading to cell propulsion overweight inter-cellular adhesion, and various signatures of glassy dynamics.

Strengths:

The model presented in the article is simple, easy to implement, and scalable. The analysis appears solid and delivers a number of clear physical properties that could be tested in more depth in experiments and future numerical studies (e.g., distribution of displacements, etc.). The authors make an appreciable effort to make contact with other models and share their ideas for further investigations.

Weaknesses:

I found two main weaknesses in the original version of this manuscript, which I strongly encourage the authors to address.

(1) The manuscript explicitly aims at resolving an apparent contradiction of tessellation-based models, such as the Vertex and the Voronoi model. Both models used the so-called shape index p0 - i.e. the ratio between the preferential perimeter and the preferential area of the cells - to drive a solid/liquid phase transition in the presence of Brownian and/or rotational noise. Specifically, for sufficiently large p0 values, these in silico cell layers undergo a transition to a state of collective migration, where a rigid junction network becomes unstable to T1 events. Because p0 is often interpreted as "adhesion strength", this leads to the paradoxical conclusion that cell intercalation is favored by intercellular adhesion. The paradox, however, only lies in this interpretation, which assigns to the shape index p0 a biophysical role that is too specific. To illustrate this concept, let us consider the energy of an individual cell of area A and perimeter P: i.e. e = (a-1)^2+c*(p-p0)^2, where a=A/A_0, with A_0 the preferred area, p=P/sqrt(A_0) and p_0 = P_0/sqrt(A_0), with P_0 the preferred perimeter. Expanding the square in the second term gives e ~ p^2 - 2p_0 p. Thus, increasing p_0, favors longer cell junctions, from which it appears reasonable to interpret p0 as a dimensionless measure of intercellular adhesion. Such an increase in the length of the junctions is, however, only a byproduct of the effect of p0 on the overall shape of the cell, which becomes progressively less rounded as p0 is increased (e.g., for a circle, p0≈3.55, for an equilateral triangle, p0≈4.56). The roundness of an individual cell, on the other hand, cannot single-handedly be ascribed to intercellular adhesion, despite intercellular adhesion being undoubtedly one of the biophysical properties affecting this geometrical feature. Moreover, the shape index p0 ​enters the energy functional at the single-cell level, implying that even in isolation, without intercellular adhesion, an increase in p0 leads to a less rounded cell morphology. These peculiarities of the Vertex/Voronoi model do raise questions about its accuracy and validity, thus justify seeking for alternative cell-resolved models such as that introduced here by Ray et al., but, on the other hand, make the interpretation of p0 as an exclusive measure of adhesion evidently dubious.

(2) The spring-bead model by Ray and coworkers has at least two predecessors in the recent literature, none of which have been cited in the present manuscript. These are Boromand et al., Phys. Rev. Lett. 121, 248003 (2018) and Pasupalak et al. arXiv:2409.16128 (2024). The former paper investigates the packing of flexible polygons and is not specific to epithelial layers, while the latter is specifically designed to address various outstanding problems in tissue mechanics, including collective migration and wound healing. While none of these models is identical to that by Ray et al., it would be fair to present the latter as a member of the family rather than the first one of its kind and possibly comment about the differences and similarities with these previous models.

Reviewer #3 (Public review):

Summary:

This is a very focused and well-performed study that uses a somewhat less common approach in the field of tissue mechanics, a deformable particle model, to propose a solution to some important phenomenological inconsistencies between the standard vertex- and SPV-model approaches and experiments. The authors' focus in their study is on the role of adhesion in glassy dynamics and solid-fluid transition of epithelia.

Strengths:

It is a carefully performed study with an important technical edge compared to "mainstream" vertex and SPV models: the ability to describe cell-cell boundaries with two distinct membranes. This may have an important implication for the phenomenology, like the role of adhesion in solid-fluid transition.

Weaknesses:

Apart from some specific suggestions for improvement and clarification, I believe the authors could do a better job in comparing their results and their approach to other similar models, such as the one by Kim et al (Reference 7).