Soft yet Sharp Interfaces in a Vertex Model of Confluent Tissue

Abstract

How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the ability of cells to independently regulate adhesivity and tension, together with neighbor-based interaction rules, lets them support strikingly unusual interfaces. In particular, we show that mechanical-and fluctuation-based measurements of the effective surface tension of a cellular aggregate yield different results, leading to mechanically soft interfaces that are nevertheless extremely sharp.The process of compartmentalizing different cell populations, and maintaining those boundaries, is of vital importance in processes ranging from early embryonic development to tumor metastasis [1,2]. A common paradigm, the differential adhesion hypothesis, treats each cell population as an immiscible fluid and suggests that cell sorting and compartmentalization are driven by an effective surface tension [3], which is in turn governed by a competition between the repulsive and adhesive interactions between cells. The precise cellular mechanisms that govern effective surface tension are still under debate; some investigations suggest it is dominated by adhesive interactions [4], while others implicate actomyosin contractility [5] or a co-regulation of these two effects [1,6,7]. It is not even clear that different methods for measuring the effective surface tension should yield consistent results, which could explain discrepancies between observations and lead to nontrivial and unexpected dynamics for cell sorting and compartmentalization.One hint that something interesting may be happening is a set of experiments demonstrating that many tissues can support extremely sharp boundaries between compartments or coexisting cell populations [1,[8][9][10][11][12]]. Here we present a possible explanation for these observations based only on the assumption that cells interact mechanically with touching neighbors, and that they might regulate these interactions differently with "unlike" cells.For simplicity, our work focuses on models for single layers of confluent cells, with no cellular gaps or overlaps. 2D vertex models represent confluent monolayers as a polygonal tiling of space where each polygon corresponds to a cell [13][14][15]; Voronoi models, which we study here, further take the cell shapes to be given by a Voronoi tessellation of the cell positions. Vertex and Voronoi models explicitly model mechanical interactions between neighboring cells, and have successfully been used to model many biophysical processes [12,[16][17][18], ranging from embryonic development to wound healing to tumor metastasis [19][20][21][22][23]. We include an additional interfacial tension between different cell types to mimic the mechanical changes that are known to occur at so-called "heterotypic" contacts. This extra term naturally leads to a mechanism for robust cell compartmentalization.Surprisingly, we find th...

Small-scale demixing in confluent biological tissues

“…Heterotypic contacts, where cells recognize neighbors of a different cell type, can be modeled in two-dimensional vertex models with a higher or lower line tension along interfaces between cells of different types, or heterotypic line tension. Such a rule results in very sharp, yet deformable, interfaces [32] where surface tension measured by macroscopic deformation of an overall droplet shape gives a value in line with equilibrium expectations, yet, surface tension measured from interfacial fluctuations is at least an order of magnitude larger. This discrepancy is due to discontinuous pinning forces generated during topological rearrangements between cells of different types.…”

“…On the other hand, recent work by some of us demonstrates that so-called heterotypic contacts in vertex models can drastically affect the notion of interfacial tension [32]. Heterotypic contacts, where cells recognize neighbors of a different cell type, can be modeled in two-dimensional vertex models with a higher or lower line tension along interfaces between cells of different types, or heterotypic line tension.…”

“…Should the answer be no, then cells must establish heterotypic interactions before sorting can occur, suggesting a more important mechanical role for cell recognition receptors than previously thought. The topological nature of the discontinuous pinning forces stabilizing interfaces in vertex model fluid mixtures tells us that once such recognition is in place, a finite amount of activity is required to overcome the discontinuity [32]. Interestingly, a recent study with both in vitro experiments and cellular Potts model simulations suggests that a large heterotypic line tension is required for cell sorting [33], although the mechanism was left unresolved.…”

Tissue flow induces cell shape changes during organogenesis

“…The third term in the Eq. 1 introduces an additional interfacial tension between different cell types i and j. γ ij is the value of the interfacial tension and l ij is the length of the interface between adjacent cells i and j [40].…”

“…For a fixed p 0 = 3.8, p droplet 0 = 3.8, γ = 5.0 and f = 1.0, we average over 100 separate simulation runs and find two characteristic relaxation timescales: t 1 = 0.251 ± 0.004 τ and t 2 = 6.381 ± 0.618 τ (average ± one standard error) where τ is the natural time unit of the simulation. Rarely, unphysical T1 transitions occurred between the artificial Voronoi cells within the droplet and generated spurious forces [40]. Hence, for averaging, we only take into account the droplets without such rearrangements.…”