Polar Fluctuations Lead to Extensile Nematic Behavior in Confluent Tissues

How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions of confluent tissues, in both liquid and solid states. Specifically, we show that a collection of microscopic constituents with no inherently nematic extensile forces can exhibit active extensile nematic behavior when subject to polar fluctuating forces. We further support our findings by performing cell level simulations of minimal models of confluent tissues.

Figure 1

Schematic of the active vertex model (AVM). The degrees of freedom are the cell vertices (black dots). Each vertex experiences two types of forces, an active force from cellular self-propulsion, ${\mathbf{f}}_i$ (red arrow), which is the mean self-propulsive force from the 3 cells that neighbor each vertex (blue arrows), and the mechanical response of the tissue to this driving, ${\mathbf{F}}_i$ (black arrow).

Figure 2

Simulation results of confluent tissues in their liquid [(a) and (b)] and solid [(c) and (d)] states. Nematic configurations, dynamics, and passive stress fields around detected $+1/2$ defects in the (a) liquid state and (c) solid state, and those of detected $-1/2$ defects in the (b) liquid state and (d) solid state. In each case, we show representative defects (left), mean velocity fields around defects (middle), and heat maps of mean isotropic passive stress $({\sigma }_{xx}+{\sigma }_{yy})/2$ due to cell-cell interactions around defects (right). Heat maps have been normalized such that blue represents maximum compression and yellow maximum tension. We use $A_0=1$, $K_A=1$, $K_P=1$, $f_0=0.5$, and $D_r=1$. In the liquid state we use $P_0=3.7$ and in the solid state $P_0=3.4$. See the Supplemental Material for details of simulation procedures and defect detection methodology [32].