Lawson-Keister, E. | bioRxiv Science

bioRxiv2022

Universal features of rigidity transitions in vertex models for biological tissues

Simple vertex models, where the cell shape is defined as a network of edges and vertices, have made useful predictions about the collective behavior of confluent biological tissues, including rigidity transitions. Quite a few different versions of vertex models have appeared in the literature, and they propose substantial differences in how the mechanical energy depends on vertex positions, yet all of them seem to make correct predictions. To understand how this is possible, we search for universality in the emergent mechanical behavior - including the shear modulus defined in the limit of zero strain rate and the viscoelastic response at finite strain rates - of six different vertex models. We identify a class of models with a well-defined shear modulus, and demonstrate that these models all exhibit a cross-over from a soft or floppy regime to a stiff regime. While the parameter that controls the crossover is different in each model, we find that the observed cell shape index (the ratio of the cell perimeter to the square root of the cell area) is a good observable order parameter for the crossover. We also find that the finite strain-rate viscoelastic response of all models exhibits a universal scaling with frequency, following the Zener model in the rigid phase and Burgers model in the fluid phase. This suggests there is a broad class of vertex models with universal mechanical features, and helps to explain why many different vertex models are able to robustly predict these features in experiments.

biophysics↗

bioRxiv2021

Collective chemotaxis in a Voronoi model for confluent clusters

Collective chemotaxis, where single cells cannot climb a biochemical signaling gradient but clusters of cells can, has been observed in different biological contexts, including confluent tissues where there are no gaps or overlaps between cells. Although particle-based models have been developed that predict important features of collective chemotaxis, the mechanisms in those models depend on particle overlaps, and so it remains unclear if they can explain behavior in confluent systems. Here, we develop an open-source code that couples a 2D Voronoi simulation for confluent cell mechanics to a dynamic chemical signal that can diffuse, advect, and/or degrade, and use the code to study potential mechanisms for collective chemotaxis in cellular monolayers. We first study the impact of advection on collective chemotaxis, and delineate a regime where advective terms are important. Next, we investigate two possible chemotactic mechanisms, contact inhibition of locomotion and heterotypic interfacial tension, and demonstrate that both can drive collective chemotaxis in certain parameter regimes. We further demonstrate that the scaling behavior of cluster motion is well-captured by simple analytic theories. 1 Statement of SignificanceThe ability of cell collectives to respond to biochemical signals, called collective chemotaxis, is crucial for many important processes including embryonic development and wound healing. We developed an open-source computational model that couples biochemical signaling gradients to confluent cell layers, where there are no gaps between cells. Our model demonstrates that two experimentally observed local cell behaviors - neighbor-induced changes to interfacial tension or a tendency of cells to repel one another after they come into contact - can drive collective chemotaxis. We also highlight a regime in which the motion of migrating cells can alter the gradient.

biophysics↗