Chiral Edge Current in Nematic Cell Monolayers

Collectively migrating cells in living organisms are often guided by their local environment, including physical barriers and internal interfaces. Well-controlled in vitro experiments have shown that, when confined in adhesive stripes, monolayers of moderately active spindle-shaped cells self-organize at well-defined angle to the stripes’ longitudinal direction and spontaneously give rise to a simple shear flow, where the average cellular orientation smoothly varies across the system. However, the impact of physical boundaries on highly active, chaotic, multicellular systems is currently unknown, despite its potential relevance. In this work, we show that human fibrosarcoma cells (HT1080) close to an interface exhibit a spontaneous edge current with broken left-right symmetry, while in the bulk the cell flow remains chaotic. These localized edge currents result from an interplay between nematic order, microscopic chirality, and topological defects. Using a combination of in vitro experiments, numerical simulations, and theoretical work, we demonstrate the presence of a self-organized layer of $+1/2$ defects anchored at the boundary and oriented at a well-defined angle close to, but smaller than, 90° with respect to the boundary direction. These self-organized defects act as local sources of chiral active stress generating the directed edge flows. Our work therefore highlights the impact of topology on the emergence of collective cell flows at boundaries. It also demonstrates the role of chirality in the emergence of edge flows. Since chirality and boundaries are common properties of multicellular systems, this work suggests a new possible mechanism for collective cellular flows.

Popular Summary

Collective migration of cancer cells in the body is routinely observed close to confining structures such as muscle fibers or blood vessels. In vitro studies recreate such behavior by showing that fibrosarcoma cells collectively migrate at the border of their colony, even though within the monolayer, cell flows obey turbulent chaotic dynamics characterized by an irregular array of vortices generated by self-propelled units. Even more surprising is that the edge currents always flow in the same direction—somehow cells collectively distinguish between their left and right near the edge. To understand this situation, we look deeper at the organization of the cells within the monolayers.

Fibrosarcoma cells are elongated and align together, defining a patchwork of well-aligned domains between which orientational singularities (topological defects) position themselves. In the bulk of the monolayer, the position and orientation of these defects randomly change over time. However, close to the boundary, we find that comet-shaped “$+1/2$ defects” orient themselves with an angle slightly smaller than 90° relative to the boundary, consistently tilting their tails to the right. Because of this left-right symmetry breaking, clockwise vortices are pushed closer to the border and generate the directed edge flow. Modeling the system as a chiral, active, nematic liquid crystal accounts well for our results and demonstrates that cell handedness is a critical ingredient for the emergence of the observed edge flows and not only for their direction.

We therefore suggest that acting on the cell handedness could interfere with collective migration of these cancer cells, which may offer new avenues in our understanding of the coupling between the handedness of single cells and collective behaviors.

Figure 1

HT1080 cell monolayer on an adhesive stripe. (a) Phase contrast image in inverted gray scale. (b) The nematic director field extracted from (a) with positive (red) and negative (blue) locations and orientations of half integer defects. (c) Black velocity streamlines are overlaid on the normalized vorticity field (blue, clockwise; red, counterclockwise). (d) Average flow along the channel shows boundary flows with net chirality. Boundary flows have a constant width independent of channel dimensions which can be observed by translating the curves onto each other. This exposes a constant decay length ($23\mu \mathrm{m}$) that can be estimated by fitting an exponential (dashed red line, $R^2=0.99$) (inset). (e) Average flow for a simulated chiral active nematic ($\alpha =-10$, $\tau =-2.5$) also shows boundary flows with net chirality and constant length scale (inset). (f) Chirality of edge flow direction in 360 fields of view is right-handed in 95% of cases and unclear in the remaining 5% of cases (see Appendix for details). (g) Average cell orientation at the edge (red) and center (blue) of the channel showing boundary alignment with a chiral tilt. (h) Average director orientation at the edge (red) and center (blue) for a simulated chiral active nematic, again with boundary alignment with a distinct chiral tilt. Simulation units and parameter values are given in the Appendix.

Figure 2

(a) Schematic of the hypothesized behavior of defects close to the boundary. Motion of $+1/2$ defects and elastic interactions lead to an accumulation of defects aligned quasiperpendicular to the left boundary. The chiral activity leads to a net flow along the boundary. (b) Average flow around $56729+1/2$ defects in a HT1080 monolayer close to the boundary (gray line) with a chiral tilt of 32.5° relative to the defect orientation (inset). (c) Average flow around $143185+1/2$ defects in a HT1080 monolayer far from the boundary with a chiral tilt of 3.4° relative to the defect orientation (inset). (d) Average flow around $+1/2$ defects made over ${10}^6$ time steps in a simulated chiral active nematic ($\alpha =-10.0$, $\tau =-1.25$) close to the left boundary (gray line). This shows a tilt relative to the average defect orientation (inset). (e) Stokeslet-like flow around an isolated chiral active $+1/2$ defect recreating tilt of 3.4° ($\tau =0.03\alpha$) relative to the defect orientation (inset). Dimensions in (b) and (c) correspond to $250\times 250\mu {\mathrm{m}}^2$.

Figure 3

(a),(b) Density of $+1/2$ defects in (a) monolayers of HT1080 cells in stripes normalized by the density at the center of the stripe and (b) simulated chiral active nematics ($\alpha =-10$, $\tau =-2.5$). For HT1080 monolayers, defect density is normalized to 1 in the bulk. (c),(d) Polar order parameter of $+1/2$ defects in (c) monolayers of HT1080 cells and (d) simulated chiral active nematics, showing orientational ordering of defects close to the boundary. (e),(f) Polar histogram of defect orientation close to the boundaries for (e) monolayers of HT1080 cells and (f) simulated chiral active nematics. The defects are on average aligned perpendicular to the boundary with a chiral tilt. In the bulk there is no net alignment (gray). Color code indicates the width of the stripe as in Fig. 1. Simulation units and parameter values are given in the Appendix.

Figure 4

(a) Average flow for simulated chiral active nematics. The net chiral flow increases in magnitude for increased chiral stress; see Fig. S7 for a close-up [39]. (b) The defect density increases with increased chiral stress. (c) The average tilt of the director close to the boundary increases with increased chiral stress. (d) Average $+1/2$ defect orientation close to the boundary. The magnitude of the chiral tilt increases with the chiral stress. Simulation units and parameter values are given in the Appendix.

Figure 5

Penetration depth $\ell$ of the chiral edge currents versus magnitude of active stresses. (a) Extensile stress $\alpha$ ($\tau =-5$) and (b) chiral stress $\tau$ ($\alpha =-10$). Insets: the average density $⟨{\rho }_{+}⟩$ of $+1/2$ defects versus the active stresses.