Motility-Driven Glass and Jamming Transitions in Biological Tissues

Abstract

Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.

Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

“…Open systems will shrink at this point so that all cells are close to their target P 0 , as shown in Fig 6a. Consistent with this, larger values of the perimeter modulus Γ lead to stronger shrinking. For fixed systems, this route is blocked, and instead there is a strong inward tension on the boundaries and a gradient in local density, as shown in Fig 6b. In agreement with the results of Bi, et al [59], we find that at low p 0 < 3.81 and low values of driving f a , cells do not take an organised pattern and do not exchange neighbours. Recast in the language of solid state physics, the tissue is in an amorphous solid or glassy state.…”

“…In order to keep the number of independent parameters to a minimum, it is again convenient to rewrite the energy of the VM, Eq (1), in a scaled form [49,59]. We first choose K i = 1 and set A 0 i ¼ p as an area scale.…”

“…There is no reason for the preferred area A 0 to be generically compatible with the preferred perimeter P 0 . This sets up a competition between the two terms in Eq (20), giving a natural scale that is determined by the relative ratio of GP Remarkably, one observes [49,59,86] a transition between a solid-like behaviour of the tissue, where cells do not exchange neighbours, and liquid-like behaviour, where neighbour exchanges do occur, at p 0 = 3.812, a value that corresponds to a regular pentagon. At present, the biological significance of this observation is not clear, but it appears to be a robust feature of many experimental systems [88].…”

Collective migration and cell jamming in asthma, cancer and development

“…But if the energy barrier might somehow be overcome, say by enhanced cellular propulsive forces, or if the energy barrier itself might somehow be diminished -or even abolished altogether -as by the mechanisms described below, then the cell could escape its cage more readily; in a variety of such cellular collectives, the characteristic scales of time and length for such cellular rearrangements have been quantified Garcia et al, 2015;Nnetu et al, 2013;Park et al, 2015b). Such events would facilitate cellular rearrangements among neighbors, and ultimately the collective as a whole could therefore unjam and flow (Bi et al, 2015(Bi et al, , 2016Park et al, 2015b). Such unjamming might be the case in the advancing of a confluent cell layer into unfilled space to heal a wound, embryonic development, morphogenesis or invasion of cancer cells into a healthy tissue Das et al, 2015;Fischer et al, 2015;Haeger et al, 2014;Serra-Picamal et al, 2012;Zheng et al, 2015).…”

Cell-to-cell variation sets a tissue-rheology–dependent bound on collective gradient sensing

“…We also established a surprising link between a central mechanical property of a cluster -its rheology -and its sensing ability. This connects mechanical transitions like unjamming [42] to sensing, opening up new areas of study. In addition, our results show cluster accuracy depends strongly on cluster rearrangement mechanism.…”